9,129 research outputs found
Statistical Mechanics and Black Hole Thermodynamics
Black holes are thermodynamic objects, but despite recent progress, the
ultimate statistical mechanical origin of black hole temperature and entropy
remains mysterious. Here I summarize an approach in which the entropy is viewed
as arising from ``would-be pure gauge'' degrees of freedom that become
dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees
of freedom can be counted, and yield the correct Bekenstein-Hawking entropy;
the corresponding problem in 3+1 dimensions remains open.Comment: 5 pages, LaTeX, uses espcrc2.sty; talk given at the Second Meeting on
Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy,
September 199
Analog quantum simulation of the Rabi model in the ultra-strong coupling regime
The quantum Rabi model describes the fundamental mechanism of light-matter
interaction. It consists of a two-level atom or qubit coupled to a quantized
harmonic mode via a transversal interaction. In the weak coupling regime, it
reduces to the well-known Jaynes-Cummings model by applying a rotating wave
approximation (RWA). The RWA breaks down in the ultra-strong coupling (USC)
regime, where the effective coupling strength is comparable to the energy
of the bosonic mode, and remarkable features in the system dynamics
are revealed. We demonstrate an analog quantum simulation of an effective
quantum Rabi model in the USC regime, achieving a relative coupling ratio of
. The quantum hardware of the simulator is a superconducting
circuit embedded in a cQED setup. We observe fast and periodic quantum state
collapses and revivals of the initial qubit state, being the most distinct
signature of the synthesized model.Comment: 20 pages, 13 figure
The Statistical Mechanics of Horizons and Black Hole Thermodynamics
Although we know that black holes are characterized by a temperature and an
entropy, we do not yet have a satisfactory microscopic ``statistical
mechanical'' explanation for black hole thermodynamics. I describe a new
approach that attributes the thermodynamic properties to ``would-be gauge''
degrees of freedom that become dynamical on the horizon. For the
(2+1)-dimensional black hole, this approach gives the correct entropy. (Talk
given at the Pacific Conference on Gravitation and Cosmology, Seoul, February
1996.)Comment: 11 pages, LaTe
The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole
In its formulation as a Chern-Simons theory, three-dimensional general
relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating
the horizon of the three-dimensional Euclidean black hole as a boundary, I
count the states of the resulting WZW model, and show that when analytically
continued back to Lorentzian signature, they yield the correct
Bekenstein-Hawking entropy. The relevant states can be understood as ``would-be
gauge'' degrees of freedom that become dynamical at the horizon.Comment: 9 pages, LaTeX. Significant sign error corrected, continuation to
Lorentzian signature clarified, several other clarifications (although
conclusion is unaffected). To appear in Phys. Rev.
The second law of quantum thermodynamics as an equality
We investigate the connection between recent results in quantum
thermodynamics and fluctuation relations by adopting a fully quantum mechanical
description of thermodynamics. By including a work system whose energy is
allowed to fluctuate, we derive a set of equalities which all thermodynamical
transitions have to satisfy. This extends the condition for maps to be
Gibbs-preserving to the case of fluctuating work, providing a more general
characterisation of maps commonly used in the information theoretic approach to
thermodynamics. For final states, block diagonal in the energy basis, this set
of equalities are necessary and sufficient conditions for a thermodynamical
state transition to be possible. The conditions serves as a parent equation
which can be used to derive a number of results. These include writing the
second law of thermodynamics as an equality featuring a fine-grained notion of
the free energy. It also yields a generalisation of the Jarzynski fluctuation
theorem which holds for arbitrary initial states, and under the most general
manipulations allowed by the laws of quantum mechanics. Furthermore, we show
that each of these relations can be seen as the quasi-classical limit of three
fully quantum identities. This allows us to consider the free energy as an
operator, and allows one to obtain more general and fully quantum fluctuation
relations from the information theoretic approach to quantum thermodynamics.Comment: 11+3 pages. V4: Updated to match published version. Discussion of
thermo-majorization and implementing arbitary unitaries added. V3: Added
funding information. V2: Expanded discussion on relation to fluctuation
theorem
Time-dependent deformation functional theory
We present a constructive derivation of a time-dependent deformation
functional theory -- a collective variable approach to the nonequalibrium
quantum many-body problem. It is shown that the motion of infinitesimal fluid
elements (i.e. a set of Lagrangian trajectories) in an interacting quantum
system is governed by a closed hydrodynamics equation with the stress force
being a universal functional of the Green's deformation tensor . Since
the Lagrangian trajectories uniquely determine the current density, this
approach can be also viewed as a representation of the time-dependent current
density functional theory. To derive the above theory we separate a
"convective" and a "relative" motions of particles by reformulating the
many-body problem in a comoving Lagrangian frame. Then we prove that a properly
defined many-body wave function (and thus any observable) in the comoving frame
is a universal functional of the deformation tensor. Both the hydrodynamic and
the Kohn-Sham formulations of the theory are presented. In the Kohn-Sham
formulation we derive a few exact representations of the exchange-correlation
potentials, and discuss their implication for the construction of new
nonadiabatic approximations. We also discuss a relation of the present approach
to a recent continuum mechanics of the incompressible quantum Hall liquids.Comment: RevTeX4, 15 page
A New Superconformal Mechanics
In this paper we propose a new supersymmetric extension of conformal
mechanics. The Grassmannian variables that we introduce are the basis of the
forms and of the vector-fields built over the symplectic space of the original
system. Our supersymmetric Hamiltonian itself turns out to have a clear
geometrical meaning being the Lie-derivative of the Hamiltonian flow of
conformal mechanics. Using superfields we derive a constraint which gives the
exact solution of the supersymmetric system in a way analogous to the
constraint in configuration space which solved the original non-supersymmetric
model. Besides the supersymmetric extension of the original Hamiltonian, we
also provide the extension of the other conformal generators present in the
original system. These extensions have also a supersymmetric character being
the square of some Grassmannian charge. We build the whole superalgebra of
these charges and analyze their closure. The representation of the even part of
this superalgebra on the odd part turns out to be integer and not spinorial in
character.Comment: Superfield re-define
Classical and quantum mechanics via supermetrics in time
Koopman-von Neumann in the 30's gave an operatorial formululation of
Classical Mechanics. It was shown later on that this formulation could also be
written in a path-integral form. We will label this functional approach as CPI
(for classical path-integral) to distinguish it from the quantum mechanical
one, which we will indicate with QPI. In the CPI two Grassmannian partners of
time make their natural appearance and in this manner time becomes something
like a three dimensional supermanifold. Next we introduce a metric in this
supermanifold and show that a particular choice of the supermetric reproduces
the CPI while a different one gives the QPI.Comment: To appear in the proceedings of the conference held in Trieste in
October 2008 with title: "Theoretical and Experimental aspects of the spin
statistics connection and related symmetries
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