Reviews of Modern Physics

In this Colloquium the theory of silicon nanowires is reviewed. Nanowires with diameters below 10   nm are the focus, where quantum effects become important and the properties diverge significantly from those of bulk silicon. These wires can be treated within electronic structure simulation m...

Current upper bounds on the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle |θ̅ |≲10⁻¹¹ . Since QCD explains a great deal of experimental data from the 100   MeV to the TeV scale, it is desirable to explain this smalln...

The fundamental physics of magnetic reconnection in laboratory and space plasmas is reviewed by discussing results from theory, numerical simulations, observations from space satellites, and recent results from laboratory plasma experiments. After a brief review of the well-known early work, represe...

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles such as the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics and did ...

This review summarizes the state of the art in searches for supersymmetry at colliders on the eve of the Large Hadron Collider era. Supersymmetry is unique among extensions of the standard model in being motivated by naturalness, dark matter, and force unification, both with and without gravity. At ...

This review provides a perspective on the recent developments in the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission in periodic hole arrays, discovered over a decade ago. It is shown that surface electro...

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein’s theory of gravity, theories that include higher-order curvature invariants, and specifically the par...

The fiber bundle model describes a collection of elastic fibers under load. The fibers fail successively and, for each failure, the load distribution among the surviving fibers changes. Even though very simple, this model captures the essentials of failure processes in a large number of materials an...

High-energy beams of charged nuclear particles (protons and heavier ions) offer significant advantages for the treatment of deep-seated local tumors in comparison to conventional megavolt photon therapy. Their physical depth-dose distribution in tissue is characterized by a small entrance dose and a...

For a few years now, cosmology has a standard model. By this term, we mean a consistent theoretical background which is at the same time simple and broad enough to offer coherent explanations for the vast majority of cosmological phenomena. This review will briefly summarize the cosmological model, ...

Many quasi-one-dimensional (1D) materials are experimental approximations to the textbook models of Peierls instabilities and collective excitations in 1D electronic systems. The recently observed self-assembly of atom wires on solid surfaces has provided fascinating new insights into the nature of ...

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entan...

This review discusses how low-energy valence excitations created by swift electrons can render information on the optical response of structured materials with unmatched spatial resolution. Electron microscopes are capable of focusing electron beams on subnanometer spots and probing the target respo...

Attempts to estimate the influence of global cosmological expansion on local systems are reviewed. Here “local” is taken to mean that the sizes of the considered systems are much smaller than cosmologically relevant scales. For example, such influences can affect orbital motions as well as confi...

Within the past 20   years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type A₂³⁺B₂⁴⁺O₇ , where A is a rare-earth ion and B is usually a transition metal. Both the A and B sites form a network of corner-sharing tetrahedra whi...

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg-Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the “distance” to the superconductor-normal phase transition line. The expansion al...

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational pro...

The potential of a Super Flavor Factory (SFF) for searches of new physics is reviewed. While very high luminosity B physics is assumed to be at the core of the program, its scope for extensive charm and τ studies are also emphasized. The possibility to run at the Υ(5S) is also discussed; in ...

Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of quantum chromodynamics. The foundations of this approach are reviewed and its application for light nuclei at various resolution scales is discussed. The e...

The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has ...

Recent progress in the field of a versatile and common system in soft matter physics, namely, star-shaped polyelectrolytes, is reviewed. These charged macromolecules combine in their properties aspects of polymer physics, colloidal science, and the rich physics of charged matter, rendering them into...

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest as they are related to important problems in information theory, such as digitalization of signa...

Investigating electronic structure and excitations under extreme conditions gives access to a rich variety of phenomena. High pressure typically induces behavior such as magnetic collapse and the insulator-metal transition in 3d transition-metal compounds, valence fluctuations or Kondo-like charac...

Materials fail by recurring rupture and shearing of interatomic bonds at microscopic, molecular scales, leading to disintegration of matter at macroscale and a loss of function. In this article, we review the state-of-the-art of investigations on failure mechanisms in materials, in particular focusing on atomistic origin of deformation and fracture and relationships between molecular mechanics and macroscale behavior. Simple examples of fracture phenomena are used to illustrate the significance and impact of material failure on our daily lives. Based on case studies, we discuss mechanisms of failure of a wide range of materials, ranging from tectonic plates to rupture of single molecules, and explain how atomistic simulation can be used to complement experimental studies and theory to provide a novel viewpoint in the analysis of complex systems. We illustrate how biological protein materials achieve extraordinary properties through intricate structures where the interplay of weak and strong chemical bonds, size and confinement effects, and hierarchical features play a fundamental role. This leads to a discussion of how even the most robust biological material systems fail, leading to diseases that arise from structural and mechanical alterations at molecular, cellular and tissue levels. We discuss new research directions in the field of materials failure and materials science and the impact of improving the current understanding of materials failure for applications in nanotechnology, biotechnology, medicine as well as the built environment.

This report reviews nearly 20 years of research related to antiferroelectric liquid crystals, and gives a short overview of possible applications. The antiferroelectric liquid crystals are the common name for smectic liquid crystals formed of chiral elongated molecules, exhibiting number of smectic tilted structures with strong tilt azimuthal direction variation from the layer to the layer (i.e. non synclinic structures). The phases have crystallographic unit periodicity ranging from few (SmC*a), four (SmC*FI2), three (SmC*FI1) and two (SmC*A) smectic layers and all of the phases posses liquid like order inside the layer. The overview describes the discovery of phases and various methods used for their identification, their structures and properties. Also theoretical understanding of these systems is given; one of the models - the discrete phenomenological model of antiferroelectric liquid crystals is discussed in details as this model allows for the most experimentally consistent explanation of phase structures and observed phase sequences under changes of temperature or external fields.

Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and AMO/quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, we describe the basics of weak continuous measurements. Particular attention is given to treating the standard quantum limit on linear amplifiers and position detectors using a general linear-response framework. We show how this approach relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics, and illustrate its application for the case of electrical circuits, including mesoscopic detectors and resonant cavity detectors.

During the past decade the interaction of light with multi-atom ensembles has attracted a lot of attention as a basic building block for quantum information processing and quantum state engineering. The field started with the realization that optically thick free space ensembles can be efficiently interfaced with quantum optical fields. By now the atomic ensemble - light interfaces have become a powerful alternative to the cavity-enhanced interaction of light with single atoms. We discuss various mechanisms used for the quantum interface, including quantum nondemolition or Faraday interaction, quantum measurement and feedback, Raman interaction and electromagnetically induced transparency. The paper provides a common theoretical frame for these processes, describes basic experimental techniques and media used for quantum interfaces, and reviews several key experiments on quantum memory for light, quantum entanglement between atomic ensembles and light, and quantum teleportation with atomic ensembles. We discuss the two types of quantum measurements which are most important for the interface: homodyne detection and photon counting. The paper concludes with an outlook on the future of atomic ensembles as an enabling technology in quantum information processing.

Investigating electronic structure and excitations under extreme conditions gives access to a rich variety of phenomena. High pressure typically induces behavior such as magnetic collapse and the insulator-metal transition in 3d transition metals compounds, valence fluctuations or Kondo-like characteristics in f-electron systems, and coordination and bonding changes in molecular solids and glasses. This article reviews research concerning electronic excitations in materials under extreme conditions using inelastic x-ray scattering (IXS). IXS is a spectroscopic probe of choice for this study because of its chemical and orbital selectivity and the richness of information it provides. Being an all-photon technique, IXS has a penetration depth compatible with high pressure requirements. Electronic transitions under pressure in 3d transition metals compounds and f-electron systems, most of them strongly correlated, are reviewed. Implications for geophysics are mentioned. Since the incident X-ray energy can easily be tuned to absorption edges, resonant IXS, often employed, is discussed at length. Finally studies involving local structure changes and electronic transitions under pressure in materials containing light elements are briefly reviewed.

In the last decade, a two-dimensional matter-light system called the microcavity exciton-polariton has emerged as a new, promising candidate of Bose Einstein Con- densation (BEC) in solids. Many pieces of important evidence of polariton BEC have been established very recently in GaAs and CdTe microcavities at the liquid Helium temperature, opening a door to rich manybody physics inaccessible in exper- iments before. Technology progress also made polariton BEC at room temperatures promising. In parallel with experimental progresses, theory and numerical simu- lations are developed, and our understanding of the system has greatly advanced. In this article, we review those recent experiments and corresponding theoretical pictures based on Gross-Pitaevskii equations and Boltzmann kinetics simulations for a finite size BEC of polaritons.

Progress over the last two decades in the theory of crystal surfaces in and out of equilibrium is reviewed. Various instabilities that occur during growth, sublimation, or are caused by elasticity, electromigration, etc... are addressed. For several geometries and nonequilibrium circumstances, a systematic derivation provides various continuum nonlinear evolution equations for driven stepped (or vicinal) surfaces. The resulting equations are sometimes different from the phenomenological equations derived from symmetry arguments, such as Kardar-Parisi-Zhang's. Some of the evolution equations are met in other nonlinear dissipative systems, while others remain unrevealed. The novel and original class of equations are referred to as "non-standard". This non-standard form suggests nontrivial dynamics, where phenomenology and symmetries, often used to infer evolution equations, fail to produce the correct form. This review focuses on step meandering and bunching, which are the two main forms of instabilities encountered on vicinal surfaces. Standard and non-standard evolution scenarios are presented using a combination of physical arguments, symmetries and systematic analysis. Other features like kinematic waves, some aspect of nucleation, and results of kinetic Monte Carlo simulations are also presented. The current state of experiments and confrontation with theories are discussed. Challenging open issues raised by the recent progress, which constitute essential future lines of inquiries, are outlined.

In this paper we review the theory of silicon nanowires. We focus on nanowires with diameters below 10nbsp;nm, where quantum effects become important and the properties diverge significantly from those of bulk silicon. These wires can be efficiently treated within electronic structure simulation methods and will be among the most important functional blocks of future nanoelectronic devices. Firstly, we review the structural properties of silicon nanowires, emphasizing the close connection between the growth orientation, the cross-section and the bounding facets. Secondly, we discuss the electronic structure of pristine and doped nanowires, which hold the ultimate key for their applicability in novel electronic devices. Finally, we review transport properties where some of the most important limitations in the performances of nanowire-based devices can lay. Many of the unique properties of these systems are at the same time defying challenges and opportunities for great technological advances.

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physically-realizable computing devices offer in principle. The field gained momentum after Peter Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review we study the information counterpart of computing. It was realized early on by Holevo, that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information, in the sense that arbitrary k-bit messages can not be compressed into messages of k-1 qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.

About 120 baryons and baryon resonances are known, from the abundant nucleon with u and d light-quark constituents up to the Xb-=(bsd) which contains one quark of each generation and to the recently discovered Wb-=(bss). In spite of this impressively large number of states, the underlying mechanisms leading to the excitation spectrum are not yet understood. Heavy-quark baryons suffer from a lack of known spin-parities. In the light-quark sector, quark-model calculations have met with considerable success in explaining the low-mass excitations spectrum but some important aspects like the mass degeneracy of positive-parity and negative-parity baryon excitations remain unclear. At high masses, above 1.8nbsp;GeV, quark models predict a very high density of resonances per mass interval which is not yet observed. In this review, issues are identified discriminating between different views of the resonance spectrum; prospects are discussed how open questions in baryon spectroscopy may find answers from photo- and electro-production experiments which are presently carried out in various laboratories. PACS: 12.39.-x; 13.60.-r; 13.75.-n; 14.20.-c

Many quasi one-dimensional (1D) materials are experimental approximations to the textbook models of Peierls instabilities and collective excitations in 1D electronic systems. The recently observed selfassembly of atom wires on solid surfaces has provided fascinating new insights into the nature of their structural and electronic instabilities, both from a real-space and momentum-space perspective. In this Colloquium, we highlight three of the most studied atom wire arrays, all featuring multiple surface state bands. One of these is made of indium atoms on a flat silicon (111) surface, while the two others consist of gold atoms on surfaces that are vicinal to Si(111). In discussing the experimental and theoretical results, we focus on the detailed mechanisms of the observed phase transitions and on the role of microscopic defects.

This review provides a perspective on the recent developments on the transmission of light through subwavelength apertures in metal films. The main focus is on the phenomenon of extraordinary optical transmission in periodic hole arrays, discovered over a decade ago. It is shown that surface electromagnetic modes play a key role in the emergence of the resonant transmission. These modes are also shown to be at the root of both the enhanced transmission and beaming of light found in single apertures surrounded by periodic corrugations. This review describes both the theoretical and the experimental aspects of the subject. For the sake of clarity, the physical mechanisms operating in the different structures considered are analyzed with a common theoretical framework. Several applications based on the transmission properties of subwavelength apertures are also addressed.

For a few years now, cosmology has a standard model. By this term, we mean a consistent theoretical background which is at the same time simple and broad enough to offer coherent explanations for the vast majority of cosmological phenomena. This review will briefly summarise the cosmological model, then proceed to discuss what we know from observations about the evolution of the Universe and its contents, and what we conclude about the origin and the future of the Universe and the structures it contains.

This review summarizes the state of the art in searches for supersymmetry at colliders on the eve of the LHC era. Supersymmetry is unique among extensions of the standard model in being motivated by naturalness, dark matter, and force unification, both with and without gravity. At the same time, weak-scale supersymmetry encompasses a wide range of experimental signals that are also found in many other frameworks. We recall the motivations for supersymmetry and review the various models and their distinctive features. We then comprehensively summarize searches for neutral and charged Higgs bosons and standard model superpartners at the high energy frontier, considering both canonical and non-canonical supersymmetric models, and including results from LEP, HERA, and the Tevatron.

We review the fundamental physics of magnetic reconnection in laboratory and space plasmas, by discussing results from theory, numerical simulations, observations from space satellites, and the recent results from laboratory plasma experiments. After a brief review of the well-known early work, we discuss representative recent experimental and theoretical work and attempt to interpret the essence of significant modern findings. In the area of local reconnection physics, many significant findings have been made with regard to two-fluid physics and are related to the cause of fast reconnection. Profiles of the neutral sheet, Hall currents, and the effects of guide field, collisions, and micro-turbulence are discussed to understand the fundamental processes in a local reconnection layer both in space and laboratory plasmas. While the understanding of the global reconnection dynamics is less developed, notable findings have been made on this issue through detailed documentation of magnetic self-organization phenomena in fusion plasmas. Application of magnetic reconnection physics to astrophysical plasmas is also briefly discussed.

High-energy beams of charged nuclear particles (protons and heavier ions) offer significant advantages for the treatment of deep-seated local tumors in comparison to conventional megavolt photon therapy. Their physical depth-dose distribution in tissue is characterized by a small entrance dose and a distinct maximum (Bragg peak) near the end of range with a sharp fall-off at the distal edge. Taking full advantage of the well-defined range and the small lateral beam spread, modern scanning beam systems allow delivery of the dose with millimeter precision. In addition, projectiles heavier than protons such as carbon ions exhibit an enhanced biological effectiveness in the Bragg peak region caused by the dense ionization of individual particle tracks resulting in reduced cellular repair. This makes them particularly attractive for the treatment of radio-resistant tumors localized near organs at risk. While tumor therapy with protons is a well established treatment modality with more than 60,000 patients treated worldwide, the application of heavy ions is so far restricted to a few facilities only. Nevertheless, results of clinical phase I-II trials provide evidence that carbon ion radiotherapy might be beneficial in several tumor entities. This article reviews the progress in heavy-ion therapy, including physical and technical developments, radiobiological studies and models as well as radiooncological studies. As a result of the promising clinical results obtained with carbon ion beams in the past 10 years at the HIMAC facility (Japan) and in a pilot project at GSI Darmstadt (Germany) the plans for new clinical centers for heavy-ion or combined proton/heavy-ion therapy have recently received a substantial boost.

The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. "Money, it's a gas." Pink Floyd, Dark Side of the Moon

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings. There remain many weak points in our theory that should be better investigated. We hope that this paper can be useful to present the state of the art of the method and to stimulate new research in this field.

The fiber bundle model describes a collection of elastic fibers under load. The fibers fail sucessively and for each failure, the load distribution among the surviving fibers changes. Even though very simple, this model captures the essentials of failure processes in a large number of materials and settings. We present here a review of the fiber bundle model with different load redistribution mechanisms from the point of view of statistics and statistical physics rather than materials science, with a focus on concepts such as criticality, universality and fluctuations. We discuss the fiber bundle model as a tool for understanding phenomena such as creep, and fatigue, how it is used to describe the behavior of fiber reinforced composites as well as modelling e.g.nbsp;network failure, traffic jams and earthquake dynamics.

Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking a nonzero value for the rest mass of photon or graviton, (3) Considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since our previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. "Dark matter" (invisible classical particles) fits well at large scales. "Modified Newtonian dynamics" provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. "Dark energy" might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. We summarize significant mass limits in a table.

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f(R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented - metric, Palatini and metric-affine - and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg - Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor - normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high Tc materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg - Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose - Einstein condensate.

Topological defects in thin films coating a deformed substrate interact with the underlying curvature. This coupling mechanism influences the shape of biological structures and provides a new strategy for the design of interfaces with prescribed functionality. In this article, we present a mathematical formalism based on the method of conformal mapping that permits the calculation of the energetics of disclinations, dislocations and vortices on rigid substrates of spatially varying Gaussian curvature. Special emphasis is placed on determining the geometric force exerted on vortices in curved superfluid films. This force, which attracts (repels) vortices towards regions of negative (positive) Gaussian curvature, is an illustration of how material shape can influence quantum mechanical degrees of freedom.