125,156 research outputs found
Quantum Mechanics and Black Holes in Four-Dimensional String Theory
In previous papers we have shown how strings in a two-dimensional target
space reconcile quantum mechanics with general relativity, thanks to an
infinite set of conserved quantum numbers, ``W-hair'', associated with
topological soliton-like states. In this paper we extend these arguments to
four dimensions, by considering explicitly the case of string black holes with
radial symmetry. The key infinite-dimensional W-symmetry is associated with the
coset structure of the dilaton-graviton sector that is a
model-independent feature of spherically symmetric four-dimensional strings.
Arguments are also given that the enormous number of string {\it discrete
(topological)} states account for the maintenance of quantum coherence during
the (non-thermal) stringy evaporation process, as well as quenching the large
Hawking-Bekenstein entropy associated with the black hole. Defining the latter
as the measure of the loss of information for an observer at infinity, who -
ignoring the higher string quantum numbers - keeps track only of the classical
mass,angular momentum and charge of the black hole, one recovers the familiar a
quadratic dependence on the black-hole mass by simple counting arguments on the
asymptotic density of string states in a linear-dilaton background.Comment: 18 page
Multidimensional entropy landscape of quantum criticality
The Third Law of Thermodynamics states that the entropy of any system in
equilibrium has to vanish at absolute zero temperature. At nonzero
temperatures, on the other hand, matter is expected to accumulate entropy near
a quantum critical point (QCP), where it undergoes a continuous transition from
one ground state to another. Here, we determine, based on general thermodynamic
principles, the spatial-dimensional profile of the entropy S near a QCP and its
steepest descent in the corresponding multidimensional stress space. We
demonstrate this approach for the canonical quantum critical compound
CeCu6-xAux near its onset of antiferromagnetic order. We are able to link the
directional stress dependence of S to the previously determined geometry of
quantum critical fluctuations. Our demonstration of the multidimensional
entropy landscape provides the foundation to understand how quantum criticality
nucleates novel phases such as high-temperature superconductivity.Comment: 14 pages, 4 figure
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
This review is devoted to the problem of thermalization in a small isolated
conglomerate of interacting constituents. A variety of physically important
systems of intensive current interest belong to this category: complex atoms,
molecules (including biological molecules), nuclei, small devices of condensed
matter and quantum optics on nano- and micro-scale, cold atoms in optical
lattices, ion traps. Physical implementations of quantum computers, where there
are many interacting qubits, also fall into this group. Statistical
regularities come into play through inter-particle interactions, which have two
fundamental components: mean field, that along with external conditions, forms
the regular component of the dynamics, and residual interactions responsible
for the complex structure of the actual stationary states. At sufficiently high
level density, the stationary states become exceedingly complicated
superpositions of simple quasiparticle excitations. At this stage, regularities
typical of quantum chaos emerge and bring in signatures of thermalization. We
describe all the stages and the results of the processes leading to
thermalization, using analytical and massive numerical examples for realistic
atomic, nuclear, and spin systems, as well as for models with random
parameters. The structure of stationary states, strength functions of simple
configurations, and concepts of entropy and temperature in application to
isolated mesoscopic systems are discussed in detail. We conclude with a
schematic discussion of the time evolution of such systems to equilibrium.Comment: 69 pages, 31 figure
Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
Highly excited many-particle states in quantum systems such as nuclei, atoms,
quantum dots, spin systems, quantum computers etc., can be considered as
``chaotic'' superpositions of mean-field basis states (Slater determinants,
products of spin or qubit states). This is due to a very high level density of
many-body states that are easily mixed by a residual interaction between
particles (quasi-particles). For such systems, we have derived simple
analytical expressions for the time dependence of energy width of wave packets,
as well as for the entropy, number of principal basis components and inverse
participation ratio, and tested them in numerical experiments. It is shown that
the energy width increases linearly and very quickly saturates.
The entropy of a system increases quadratically, at small
times, and after, can grow linearly, , before the saturation.
Correspondingly, the number of principal components determined by the entropy,
, or by the inverse participation ratio, increases
exponentially fast before the saturation. These results are explained in terms
of a cascade model which describes the flow of excitation in the Fock space of
basis components. Finally, a striking phenomenon of damped oscillations in the
Fock space at the transition to an equilibrium is discussed.Comment: RevTex, 14 pages including 12 eps-figure
Lyapunov exponents, entropy production and decoherence
We establish that the entropy production rate of a classically chaotic
Hamiltonian system coupled to the environment settles, after a transient, to a
meta-stable value given by the sum of positive generalized Lyapunov exponents.
A meta-stable steady state is generated in this process. This behavior also
occurs in quantum systems close to the classical limit where it leads to the
restoration of quantum-classical correspondence in chaotic systems coupled to
the environment.Comment: 4 ReVTeX pages + 3 postscript figures. PRL (to appear
Evaluation of configurational entropy of a model liquid from computer simulations
Computer simulations have been employed in recent years to evaluate the
configurational entropy changes in model glass-forming liquids. We consider two
methods, both of which involve the calculation of the `intra-basin' entropy as
a means for obtaining the configurational entropy. The first method involves
the evaluation of the intra-basin entropy from the vibrational frequencies of
inherent structures, by making a harmonic approximation of the local potential
energy topography. The second method employs simulations that confine the
liquid within a localized region of configuration space by the imposition of
constraints; apart from the choice of the constraints, no further assumptions
are made. We compare the configurational entropies estimated for a model liquid
(binary mixture of particles interacting {\it via} the Lennard-Jones potential)
for a range of temperatures, at fixed density.Comment: 10 pages, 5 figures, Proceedings of "Unifying Concepts in Glass
Physics" Trieste 1999 (to appear in J. Phys. Cond. Mat.
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