scholarly journals Localization of quantum topology in the presence of matter and gauge fields

2015 ◽  
Vol 12 (09) ◽  
pp. 1550091
Author(s):  
Farzaneh Atyabi
Keyword(s):  
Boundary Condition ◽  
Hilbert Space ◽  
Gauge Field ◽  
Quantum Particle ◽  
Spectral Geometry ◽  
Gauge Fields ◽  
Fuzzy Topology ◽  
One Dimensional ◽  
Quantum Topology ◽  
Large N

In this paper a toy model of quantum topology is reviewed to study effects of matter and gauge fields on the topology fluctuations. In the model a collection of N one-dimensional manifolds is considered where a set of boundary conditions on states of Hilbert space specifies a set of all topologies perceived by quantum particle and probability of having a specific topology is determined by a partition function over all the topologies in the context of noncommutative spectral geometry. In general the topologies will be fuzzy with the exception of a particular case which is localized by imposing a specific boundary condition. Here fermions and bosons are added to the model. It is shown that in the presence of matter, the fuzziness of topology will be dependent on N, however for large N the dependence is removed similar to the case without matter. Also turning on a particular background gauge field can overcome the fuzziness of topology to reach a localized topology with classical interpretation. It can be seen that for large N more opportunities can be provided for choosing the background gauge field to localize the fuzzy topology.

scholarly journals MULTIPLE CHERN–SIMONS FIELDS ON A TORUS

1994 ◽  
Vol 09 (06) ◽  
pp. 969-989 ◽  
Author(s):  
DENNE WESOLOWSKI ◽  
YUTAKA HOSOTANI ◽  
CHOON-LIN HO
Keyword(s):  
Hilbert Space ◽  
Gauge Field ◽  
Wilson Line ◽  
Wave Functions ◽  
Effective Theory ◽  
Gauge Fields ◽  
Vacuum Structure ◽  
Vacuum Degeneracy ◽  
Chern Simons

Intertwined multiple Chern–Simons gauge fields induce matrix statistics among particles. We analyze this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an effective theory with one Chern–Simons gauge field. The correspondence between the Wilson line integrals, vacuum degeneracy and wave functions for these two theories are discussed. Further, it is found in both of these cases that the two total momenta and Hamiltonian commute only in the physical Hilbert space.

scholarly journals Atom-optically synthetic gauge fields for a noninteracting Bose gas

2022 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuqing Li ◽  
Jiahui Zhang ◽  
Yunfei Wang ◽  
Huiying Du ◽  
Jizhou Wu ◽  
...  
Keyword(s):  
Gauge Field ◽  
Feshbach Resonance ◽  
Bose Gas ◽  
Gauge Fields ◽  
Experimental Realization ◽  
Momentum State ◽  
One Dimensional ◽  
Atomic Transport ◽  
Synthetic Gauge Fields ◽  
Topological Phases Of Matter

AbstractSynthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of 133Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Analysis for the Effect of Inverter Ripple Current on Fuel Cell Operating Condition

2001 ◽  
Author(s):  
Randall S. Gemmen
Keyword(s):  
Boundary Condition ◽  
Fuel Cell ◽  
Mass Transport ◽  
Transient Behavior ◽  
Mechanical State ◽  
Dimensional Model ◽  
One Dimensional ◽  
Fuel Cell Stack ◽  
A Cell ◽  
The Impact

Abstract The effect of inverter ripple current on fuel cell stack performance and stack lifetime remains uncertain. This paper provides a first attempt to examine the impact of inverter load dynamics on the fuel cell. Since reactant utilization is known to impact the mechanical state of a fuel cell, it is suggested that the varying reactant conditions surrounding the cell govern, at least in part, the lifetime of the cells. This paper investigates these conditions through the use of a dynamic model for the bulk conditions within the stack, as well as a one-dimensional model for the detailed mass transport occurring within the electrode of a cell. These two independent modeling approaches help to verify their respective numerical procedures. In this work, the inverter load is imposed as a boundary condition to the models. Results show the transient behavior of the reactant concentrations within the stack, and of the mass diffusion within the electrode under inverter loads with frequencies between 30 Hz and 1250 Hz.

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