124,811 research outputs found
Deformed Jarzynski Equality
The well-known Jarzynski equality, often written in the form , provides a non-equilibrium means to measure
the free energy difference of a system at the same inverse
temperature based on an ensemble average of non-equilibrium work .
The accuracy of Jarzynski's measurement scheme was known to be determined by
the variance of exponential work, denoted as . However, it was recently found that can systematically diverge in both classical and quantum cases. Such
divergence will necessarily pose a challenge in the applications of Jarzynski
equality because it may dramatically reduce the efficiency in determining
. In this work, we present a deformed Jarzynski equality for both
classical and quantum non-equilibrium statistics, in efforts to reuse
experimental data that already suffers from a diverging . The main feature of our deformed Jarzynski
equality is that it connects free energies at different temperatures and it may
still work efficiently subject to a diverging . The conditions for applying our deformed Jarzynski equality may be
met in experimental and computational situations. If so, then there is no need
to redesign experimental or simulation methods. Furthermore, using the deformed
Jarzynski equality, we exemplify the distinct behaviors of classical and
quantum work fluctuations for the case of a time-dependent driven harmonic
oscillator dynamics and provide insights into the essential performance
differences between classical and quantum Jarzynski equalities.Comment: 24 pages, 1 figure, accepted version to appear in Entropy (Special
Issue on "Quantum Thermodynamics"
Developments in Random Matrix Theory
In this preface to the Journal of Physics A, Special Edition on Random Matrix
Theory, we give a review of the main historical developments of random matrix
theory. A short summary of the papers that appear in this special edition is
also given.Comment: 22 pages, Late
On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
Correlation functions involving products and ratios of half-integer powers of
characteristic polynomials of random matrices from the Gaussian Orthogonal
Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT)
to physics of quantum chaotic systems, and beyond. We provide an explicit
evaluation of the large- limits of a few non-trivial objects of that sort
within a variant of the supersymmetry formalism, and via a related but
different method. As one of the applications we derive the distribution of an
off-diagonal entry of the resolvent (or Wigner -matrix) of GOE
matrices which, among other things, is of relevance for experiments on chaotic
wave scattering in electromagnetic resonators.Comment: 25 pages (2 figures); published version (conclusion added, minor
changes
Stable Feature Selection for Biomarker Discovery
Feature selection techniques have been used as the workhorse in biomarker
discovery applications for a long time. Surprisingly, the stability of feature
selection with respect to sampling variations has long been under-considered.
It is only until recently that this issue has received more and more attention.
In this article, we review existing stable feature selection methods for
biomarker discovery using a generic hierarchal framework. We have two
objectives: (1) providing an overview on this new yet fast growing topic for a
convenient reference; (2) categorizing existing methods under an expandable
framework for future research and development
Generalized Quantum Dynamics as Pre-Quantum Mechanics
We address the issue of when generalized quantum dynamics, which is a
classical symplectic dynamics for noncommuting operator phase space variables
based on a graded total trace Hamiltonian , reduces to Heisenberg
picture complex quantum mechanics. We begin by showing that when , with a Weyl ordered operator Hamiltonian, then the generalized
quantum dynamics operator equations of motion agree with those obtained from
in the Heisenberg picture by using canonical commutation relations. The
remainder of the paper is devoted to a study of how an effective canonical
algebra can arise, without this condition simply being imposed by fiat on the
operator initial values. We first show that for any total trace Hamiltonian
which involves no noncommutative constants, there is a conserved
anti--self--adjoint operator with a structure which is closely
related to the canonical commutator algebra. We study the canonical
transformations of generalized quantum dynamics, and show that is a
canonical invariant, as is the operator phase space volume element. The latter
result is a generalization of Liouville's theorem, and permits the application
of statistical mechanical methods to determine the canonical ensemble governing
the equilibrium distribution of operator initial values. We give arguments
based on a Ward identity analogous to the equipartition theorem of classical
statistical mechanics, suggesting that statistical ensemble averages of Weyl
ordered polynomials in the operator phase space variables correspond to the
Wightman functions of a unitary complex quantum mechanics, with a conserved
operator Hamiltonian and with the standard canonical commutation relations
obeyed by Weyl ordered operator strings. Thus there is a well--defined sense inComment: 79 pages, no figures, plain te
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