232 research outputs found
Local and Effective Temperatures of Quantum Driven Systems
We introduce thermometers to define the local temperature of an electronic
system driven out-of-equilibrium by local AC fields. We also define the
effective temperature in terms of a local fluctuation-dissipation-relation. We
show that within the weak driving regime these two temperatures coincide. We
also discuss the behavior of the local temperature along the sample. We show
that it exhibits spatial fluctuations following an oscillatory pattern. For
weak driving, regions of the sample become heated, while others become cooled
as a consequence of the driving
Magnetic structures and Z_2 vortices in a non-Abelian gauge model
The magnetic order of the triangular lattice with antiferromagnetic
interactions is described by an SO(3) field and allows for the presence of Z2
magnetic vortices as defects. In this work we show how these Z2 vortices can be
fitted into a local SU(2) gauge theory. We propose simple Ansatzes for vortex
configurations and calculate their energies using well-known results of the
Abelian gauge model. We comment on how Dzyaloshinskii-Moriya interactions could
be derived from a non-Abelian gauge theory and speculate on their effect on non
trivial configurations
Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretisation schemes
We introduce a numerical method to integrate the stochastic
Landau-Lifshitz-Gilbert equation in spherical coordinates for generic
discretization schemes. This method conserves the magnetization modulus and
ensures the approach to equilibrium under the expected conditions. We test the
algorithm on a benchmark problem: the dynamics of a uniformly magnetized
ellipsoid. We investigate the influence of various parameters, and in
particular, we analyze the efficiency of the numerical integration, in terms of
the number of steps needed to reach a chosen long time with a given accuracy.Comment: 9 pages and 7 figure
Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model
We study the Hamiltonian dynamics of the spherical spin model with
fully-connected two-body interactions drawn from a Gaussian probability
distribution. In the statistical physics framework, the potential energy is of
the so-called spherical disordered kind. Most importantly for our
setting, the energy conserving dynamics are equivalent to the ones of the
Neumann integrable system. We take initial conditions in thermal equilibrium
and we subsequently evolve the configurations with Newton dynamics dictated by
a different Hamiltonian. We identify three dynamical phases depending on the
parameters that characterise the initial state and the final Hamiltonian. We
obtain the {\it global} dynamical observables with numerical and analytic
methods and we show that, in most cases, they are out of thermal equilibrium.
We note, however, that for shallow quenches from the condensed phase the
dynamics are close to (though not at) thermal equilibrium. Surprisingly enough,
for a particular relation between parameters the global observables comply
Gibbs-Boltzmann equilibrium. We next set the analysis of the system with finite
number of degrees of freedom in terms of non-linearly coupled modes. We
evaluate the mode temperatures and we relate them to the frequency-dependent
effective temperature measured with the fluctuation-dissipation relation in the
frequency domain, similarly to what was recently proposed for quantum
integrable cases. Finally, we analyse the integrals of motion and we use
them to show that the system is out of equilibrium in all phases, even for
parameters that show an apparent Gibbs-Boltzmann behaviour of global
observables. We elaborate on the role played by these constants of motion in
the post-quench dynamics and we briefly discuss the possible description of the
asymptotic dynamics in terms of a Generalised Gibbs Ensemble
Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
We construct a path-integral representation of the generating functional for
the dissipative dynamics of a classical magnetic moment as described by the
stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by
Brown, with the possible addition of spin-torque terms. In the process of
constructing this functional in the Cartesian coordinate system, we critically
revisit this stochastic equation. We present it in a form that accommodates for
any discretization scheme thanks to the inclusion of a drift term. The
generalized equation ensures the conservation of the magnetization modulus and
the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential
and time-dependent forces. The drift term vanishes only if the mid-point
Stratonovich prescription is used. We next reset the problem in the more
natural spherical coordinate system. We show that the noise transforms
non-trivially to spherical coordinates acquiring a non-vanishing mean value in
this coordinate system, a fact that has been often overlooked in the
literature. We next construct the generating functional formalism in this
system of coordinates for any discretization prescription. The functional
formalism in Cartesian or spherical coordinates should serve as a starting
point to study different aspects of the out-of-equilibrium dynamics of magnets.
Extensions to colored noise, micro-magnetism and disordered problems are
straightforward.Comment: 47 pages + appendix, published versio
Vortex solutions in the noncommutative torus
Vortex configurations in the two-dimensional torus are considered in
noncommutative space. We analyze the BPS equations of the Abelian Higgs model.
Numerical solutions are constructed for the self-dual and anti-self dual cases
by extending an algorithm originally developed for ordinary commutative space.
We work within the Fock space approach to noncommutative theories and the
Moyal-Weyl connection is used in the final stage to express the solutions in
configuration space.Comment: 18 pages, 5 figure
Relation Between Local Temperature Gradients and the Direction of Heat Flow in Quantum Driven Systems
We introduce thermometers to define the local temperature of an electronic
system driven out-of-equilibrium by local ac fields. We discuss the behavior of
the local temperature along the sample, showing that it exhibits spatial
fluctuations following an oscillatory pattern. We show explicitly that the
local temperature is the correct indicator for heat flow.Comment: 3 pages, 2 figure
(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
We study a classical integrable (Neumann) model describing the motion of a
particle on the sphere, subject to harmonic forces. We tackle the problem in
the infinite dimensional limit by introducing a soft version in which the
spherical constraint is imposed only on average over initial conditions. We
show that the Generalized Gibbs Ensemble captures the long-time averages of the
soft model. We reveal the full dynamic phase diagram with extended,
quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The
scaling properties of the fluctuations allow us to establish in which cases the
strict and soft spherical constraints are equivalent, confirming the validity
of the GGE hypothesis for the Neumann model on a large portion of the dynamic
phase diagram.Comment: 5 pages, 3 figure
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