180,106 research outputs found
Links between Dissipation and R\'{e}nyi Divergences in -Symmetric Quantum Mechanics
Thermodynamics and information theory have been intimately related since the
times of Maxwell and Boltzmann. Recently it was shown that the dissipated work
in an arbitrary non-equilibrium process is related to the R\'{e}nyi divergences
between two states along the forward and reversed dynamics. Here we show that
the relation between dissipated work and Renyi divergences generalizes to
-symmetric quantum mechanics with unbroken
symmetry. In the regime of broken symmetry, the relation between
dissipated work and Renyi divergences does not hold as the norm is not
preserved during the dynamics. This finding is illustrated for an
experimentally relevant system of two-coupled cavities.Comment: 7 page
Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
In this work, we establish a general theory of phase transitions and quantum
entanglement in the equilibrium state at arbitrary temperatures. First, we
derived a set of universal functional relations between the matrix elements of
two-body reduced density matrix of the canonical density matrix and the
Helmholtz free energy of the equilibrium state, which implies that the
Helmholtz free energy and its derivatives are directly related to entanglement
measures because any entanglement measures are defined as a function of the
reduced density matrix. Then we show that the first order phase transitions are
signaled by the matrix elements of reduced density matrix while the second
order phase transitions are witnessed by the first derivatives of the reduced
density matrix elements. Near second order phase transition point, we show that
the first derivative of the reduced density matrix elements present universal
scaling behaviors. Finally we establish a theorem which connects the phase
transitions and entanglement at arbitrary temperatures. Our general results are
demonstrated in an experimentally relevant many-body spin model.Comment: 8 pages,2 figure
Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble
In this work, we investigate the heat exchange between two quantum systems
whose initial equilibrium states are described by the generalized Gibbs
ensemble. First, we generalize the fluctuation relations for heat exchange
discovered by Jarzynski and W\'ojcik to quantum systems prepared in the
equilibrium states described by the generalized Gibbs ensemble at different
generalized temperatures. Second, we extend the connections between heat
exchange and R\'enyi divergences to quantum systems with very general initial
conditions.These relations are applicable for quantum systems with conserved
quantities and are universally valid for quantum systems in the integrable and
chaotic regimes.Comment: 7 page
Insights into Phase Transitions and Entanglement from Density Functional Theory
Density functional theory has made great success in solid state physics,
quantum chemistry and in computational material sciences. In this work we show
that density functional theory could shed light on phase transitions and
entanglement at finite temperatures. Specifically, we show that the equilibrium
state of an interacting quantum many-body system which is in thermal
equilibrium with a heat bath at a fixed temperature is a universal functional
of the first derivatives of the free energy with respect to temperature and
other control parameters respectively. This insight from density functional
theory enables us to express the average value of any physical observable and
any entanglement measure as a universal functional of the first derivatives of
the free energy with respect to temperature and other control parameters. Since
phase transitions are marked by the nonanalytic behavior of free energy with
respect to control parameters, the physical quantities and entanglement
measures may present nonanalytic behavior at critical point inherited from
their dependence on the first derivative of free energy. We use an
experimentally realizable model to demonstrate the idea. These results give new
insights for phase transitions and provide new profound connections between
entanglement and phase transition in interacting quantum many-body physics.Comment: 10 pages, 5 figure
Quantum Work Relations and Response Theory in -Symmetric Quantum Systems
In this work, we show that a universal quantum work relation for a quantum
system driven arbitrarily far from equilibrium extend to
-symmetric quantum system with unbroken symmetry,
which is a consequence of microscopic reversibility. The quantum Jarzynski
equality, linear response theory and Onsager reciprocal relations for the
-symmetric quantum system are recovered as special cases of the
universal quantum work relation in -symmetric quantum system. In
the regime of broken symmetry, the universal quantum work
relation does not hold as the norm is not preserved during the dynamics.Comment: 6 page
Dissipation in the Generalized Gibbs Ensemble
In this work, we show that the dissipation in a many-body system under an
arbitrary non-equilibrium process is related to the R\'{e}nyi divergences
between two states along the forward and reversed dynamics under very general
family of initial conditions. This relation generalizes the links between
dissipated work and Renyi divergences to quantum systems with conserved
quantities whose equilibrium state is described by the generalized Gibbs
ensemble. The relation is applicable for quantum systems with conserved
quantities and can be applied to protocols driving the system between
integrable and chaotic regimes. We demonstrate our ideas by considering the
one-dimensional transverse quantum Ising model which is driven out of
equilibrium by the instantaneous switching of the transverse magnetic field.Comment: 6 pages. arXiv admin note: text overlap with arXiv:1710.0605
Relations between Heat Exchange and R\'{e}nyi Divergences
In this work, we establish an exact relation which connects the heat exchange
between two systems initialized in their thermodynamic equilibrium states at
different temperatures and the R\'{e}nyi divergences between the initial
thermodynamic equilibrium state and the final non-equilibrium state of the
total system. The relation tells us that the various moments of the heat
statistics are determined by the Renyi divergences between the initial
equilibrium state and the final non-equilibrium state of the global system. In
particular the average heat exchange is quantified by the relative entropy
between the initial equilibrium state and the final non-equilibrium state of
the global system. The relation is applicable to both finite classical systems
and finite quantum systems.Comment: 5 page
The statistic thermodynamical entropy of de Sitter space and it's 1-loop correction
From the partition function of canonical ensemble we derive the entropy of
the de Sitter space by anti-Wick rotation. And then from the one-loop bubble
created from vacuum fluctuation in de Sitter background space,
we obtain the one-loop quantum correction to the entropy of de Sitter space.Comment: 10 pages, 0 figure
Relations between Dissipated Work and R\'enyi Divergences
In this paper, we establish a general relation which directly links the
dissipated work done on a system driven arbitrarily far from equilibrium, a
fundamental quantity in thermodynamics, and the R\'{e}nyi divergences, a
fundamental concept in information theory. Specifically, we find that the
generating function of the dissipated work under an arbitrary time-dependent
driving process is related to the R\'{e}nyi divergences between a
non-equilibrium state in the driven process and a non-equilibrium state in its
time reversed process. This relation is a consequence of time reversal symmetry
in driven process and is universally applicable to both finite classical system
and finite quantum system, arbitrarily far from equilibrium.Comment: 5 pages and 2 figure
Fidelity Susceptibility in the Quantum Rabi Model
Quantum criticality usually occurs in many-body systems. Recently it was
shown that the quantum Rabi model, which describes a two-level atom coupled to
a single model cavity field, presents quantum phase transitions from a normal
phase to a superradiate phase when the ratio between the frequency of the two
level atom and the frequency of the cavity field extends to infinity. In this
work, we study quantum phase transitions in the quantum Rabi model from the
fidelity susceptibility perspective. We found that the fidelity susceptibility
and the generalized adiabatic susceptibility present universal finite size
scaling behaviors near the quantum critical point of the Rabi model if the
ratio between frequency of the two level atom and frequency of the cavity field
is finite. From the finite size scaling analysis of the fidelity
susceptibility, we found that the adiabatic dimension of the fidelity
susceptibility and the generalized adiabatic susceptibility of fourth order in
the Rabi model are and , respectively. Meanwhile the correlation
length critical exponent and the dynamical critical exponent in the quantum
critical point of the Rabi model are found to be and respectively.
Since the fidelity susceptibility and the generalized adiabatic susceptibility
are the moments of the quantum noise spectrum which is directly measurable by
experiments in linear response regime, the scaling behavior of the fidelity
susceptibility in the Rabi model could be tested experimentally. The simple
structure of the quantum Rabi model paves the way for experimentally observing
the universal scaling behavior of the fidelity susceptibility at a quantum
phase transition.Comment: 6 pages, 6 Figure
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