The geometric phase and the spin-statistics relation

2010 ◽  
Vol 466 (2122) ◽  
pp. 2917-2932 ◽  
Author(s):  
P. Bandyopadhyay
Keyword(s):  
Geometric Phase ◽  
Degrees Of Freedom ◽  
Berry Phase ◽  
Scalar Particle ◽  
Quantum Spin ◽  
Point Of View ◽  
Stochastic Mechanics ◽  
Magnetic Flux Quantum ◽  
Spin Basis ◽  
Time Point

The exchange phase for two spins is studied here from the point of view of the quantization of a fermion in the framework of Nelson’s stochastic mechanics. This introduces a direction vector attached to a space–time point depicting the spin degrees of freedom. In this formalism, a fermion appears as a scalar particle attached with a magnetic-flux quantum, and a quantum spin can be described in terms of an SU(2) gauge bundle. This helps us to recast the Berry–Robbins formalism where the exchange phase appears as an unfamiliar geometric phase arising out of the ‘exchange rotation’ in a transported spin basis in terms of gauge currents. However, for polarized fermions, the exchange phase is found to be given by the Berry phase.

scholarly journals The geometric phase and the geometrodynamics of relativistic electron vortex beams

2014 ◽  
Vol 470 (2163) ◽  
pp. 20130525 ◽  
Author(s):  
Pratul Bandyopadhyay ◽  
Banasri Basu ◽  
Debashree Chowdhury
Keyword(s):  
Relativistic Electron ◽  
Geometric Phase ◽  
Vortex Line ◽  
Degrees Of Freedom ◽  
Berry Phase ◽  
Scalar Particle ◽  
Propagation Direction ◽  
Dirac Monopole ◽  
Vortex Beams ◽  
Group Flow

We have studied here the geometrodynamics of relativistic electron vortex beams from the perspective of the geometric phase associated with the scalar electron encircling the vortex line. It is pointed out that the electron vortex beam carrying orbital angular momentum is a natural consequence of the skyrmion model of a fermion. This follows from the quantization procedure of a fermion in the framework of Nelson's stochastic mechanics when a direction vector (vortex line) is introduced to depict the spin degrees of freedom. In this formalism, a fermion is depicted as a scalar particle encircling a vortex line. It is here shown that when the Berry phase acquired by the scalar electron encircling the vortex line involves quantized Dirac monopole, we have paraxial (non-paraxial) beam when the vortex line is parallel (orthogonal) to the wavefront propagation direction. Non-paraxial beams incorporate spin–orbit interaction. When the vortex line is tilted with respect to the propagation direction, the Berry phase involves non-quantized monopole. The temporal variation of the direction of the tilted vortices is studied here taking into account the renormalization group flow of the monopole charge and it is predicted that this gives rise to the spin Hall effect.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

scholarly journals Topological Quantum Computing and 3-Manifolds

2021 ◽  
Vol 3 (1) ◽  
pp. 153-165
Author(s):  
Torsten Asselmeyer-Maluga
Keyword(s):  
Quantum Computing ◽  
Berry Phase ◽  
Basic Structure ◽  
Quantum States ◽  
Point Of View ◽  
Surface Topology ◽  
Usual Sense ◽  
Closed Curves ◽  
Topological Quantum ◽  
2D System

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston’s geometrization theorem gives the main description of 3-dimensional manifolds. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere. The whole system depends strongly on the topology of this complement, which is determined by non-contractible, closed curves. Every curve gives a contribution to the quantum states by a phase (Berry phase). Therefore, the quantum states can be manipulated by using the knot group (fundamental group of the knot complement). The universality of these operations was already showed by M. Planat et al.

DARK GEOMETRY

2004 ◽  
Vol 13 (10) ◽  
pp. 2275-2279 ◽  
Author(s):  
J. A. R. CEMBRANOS ◽  
A. DOBADO ◽  
A. L. MAROTO
Keyword(s):  
Dark Matter ◽  
Extra Dimensions ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Point Of View ◽  
Missing Mass ◽  
Brane Worlds ◽  
Mass Problem ◽  
Extra Space ◽  
The Universe

Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space–time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

scholarly journals Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors

2019 ◽  
Vol 7 (1) ◽  
pp. 12-20 ◽  
Author(s):  
Hongyi Yu ◽  
Mingxing Chen ◽  
Wang Yao
Keyword(s):  
Magnetic Field ◽  
Berry Phase ◽  
Transition Metal Dichalcogenides ◽  
Real Space ◽  
Quantum Spin ◽  
Moire Patterns ◽  
Metal Dichalcogenides ◽  
Berry Phases ◽  
Different Origins ◽  
Moiré Patterns

Abstract When quasiparticles move in condensed matters, the texture of their internal quantum structure as a function of position and momentum can give rise to Berry phases that have profound effects on the material’s properties. Seminal examples include the anomalous Hall and spin Hall effects from the momentum-space Berry phases in homogeneous crystals. Here, we explore a conjugate form of the electron Berry phase arising from the moiré pattern: the texture of atomic configurations in real space. In homobilayer transition metal dichalcogenides, we show that the real-space Berry phase from moiré patterns manifests as a periodic magnetic field with magnitudes of up to hundreds of Tesla. This quantity distinguishes moiré patterns from different origins, which can have an identical potential landscape, but opposite quantized magnetic flux per supercell. For low-energy carriers, the homobilayer moirés realize topological flux lattices for the quantum-spin Hall effect. An interlayer bias can continuously tune the spatial profile of the moiré magnetic field, whereas the flux per supercell is a topological quantity that can only have a quantized jump observable at a moderate bias. We also reveal the important role of the non-Abelian Berry phase in shaping the energy landscape in small moiré patterns. Our work points to new possibilities to access ultra-high magnetic fields that can be tailored to the nanoscale by electrical and mechanical controls.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES

2010 ◽  
Vol 02 (03n04) ◽  
pp. 217-234
Author(s):  
IOANNIS STEFANOU ◽  
JEAN SULEM
Keyword(s):  
Mechanical Properties ◽  
Discrete System ◽  
Degrees Of Freedom ◽  
Fractured Rock ◽  
Three Dimensional ◽  
Cosserat Continuum ◽  
Point Of View ◽  
Rock Masses ◽  
Homogenization Technique ◽  
Rock Structure

The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

KINEMATICS FEATURES OF HAMMER PERFORATED TILLAGE ROLL

2020 ◽  
pp. 13-19
Author(s):  
I. А. Sharonov ◽  
◽  
Yu. М. Isaev ◽  
V. I. Kurdyumov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Soil Layer ◽  
Point Of View ◽  
Lagrange Equations ◽  
Middle Volga Region ◽  
Perforated Cylinder ◽  
Winter Crops ◽  
Combined Impact ◽  
The Impact

The task of improving the quality of agricultural tools by improving the technological processes of their functioning, taking into account the kinematic features of the combined impact of working elements of tools on the soil environment is important from a scientific and technical point of view. To form the required structure and density of the soil layer at the depth of sowing, a hammer perforated tillage roller (HPTR) has been developed. The study aim is to improve the quality of post-sowing compaction and structuring of the soil layer in the seed location zone based on the development of an innovative design of HPTR that combines different effects on the treated environment. The object of research is the kinematic mode of operation of the HPTR, equipped with cylindrical hammers installed at the ends of the rod, which, in turn, are radially and pivotally installed on the axis of the gunFeature of offered HPTR is the excitation of hammer vibrations, which changes the kinematic parameters of the tillage tool as a whole. Lagrange equations of the second kind are used to describe the process of HPTR operation, which is represented as a system of material objects with several degrees of freedom. The conducted studies revealed the periodic nature of changes in the strength of the impact of HPTR on the soil. The obtained equations allow us to determine the features of the HPTR movement at different masses of a hollow perforated cylinder and cylindrical hammers. This is of great importance for increasing the efficiency of soil bolster destruction and creating the soil structure recommended for winter crops sown in the Middle Volga region.

scholarly journals Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Christoph P. Hofmann
Keyword(s):  
Partition Function ◽  
Degrees Of Freedom ◽  
Spatial Dimension ◽  
Lagrangian Method ◽  
Point Of View ◽  
Low Energy ◽  
Effective Theory ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Spatial Dimensions

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

BERRY PHASE IN COUPLED TWO-LEVEL SYSTEMS

2013 ◽  
Vol 27 (12) ◽  
pp. 1350088 ◽  
Author(s):  
X. Y. ZHANG ◽  
J. H. TENG ◽  
X. X. YI
Keyword(s):  
Asymptotic Behavior ◽  
Geometric Phase ◽  
Berry Phase ◽  
External Control ◽  
Control Parameters ◽  
Coupling Constant ◽  
Geometric Phases ◽  
Coupled Subsystems ◽  
Two Level Systems ◽  
The Individual

The application of geometric phases into robust control of quantal systems has triggered exploration of the geometric phase for coupled subsystems. Earlier studies have mainly focused on the situation where the external control parameters are in the free Hamiltonian of the subsystems, i.e. the controls exert only on the individual subsystems. Here we consider another circumstance that we can control the coupling geiϕ between the subsystems. By changing only the phase ϕ in the coupling constant, we derive the Berry phase acquired by the system and compare it to the geometric phase acquired by changing the coupling strength g. We find that the asymptotic behavior of the Berry phase depends on the relative Rabi frequency of the two subsystems, and it approaches π when the amplitude of the coupling tends to infinity.

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