1,611 research outputs found

### Generalized rotating-wave approximation for arbitrarily large coupling

A generalized version of the rotating-wave approximation for the single-mode
spin-boson Hamiltonian is presented. It is shown that performing a simple
change of basis prior to eliminating the off-resonant terms results in a
significantly more accurate expression for the energy levels of the system. The
generalized approximation works for all values of the coupling strength and for
a wide range of detuning values, and may find applications in solid-state
experiments.Comment: 4 pages, 2 figs, REVTeX

### Microcanonical Origin of the Maximum Entropy Principle for Open Systems

The canonical ensemble describes an open system in equilibrium with a heat
bath of fixed temperature. The probability distribution of such a system, the
Boltzmann distribution, is derived from the uniform probability distribution of
the closed universe consisting of the open system and the heat bath, by taking
the limit where the heat bath is much larger than the system of interest.
Alternatively, the Boltzmann distribution can be derived from the Maximum
Entropy Principle, where the Gibbs-Shannon entropy is maximized under the
constraint that the mean energy of the open system is fixed. To make the
connection between these two apparently distinct methods for deriving the
Boltzmann distribution, it is first shown that the uniform distribution for a
microcanonical distribution is obtained from the Maximum Entropy Principle
applied to a closed system. Then I show that the target function in the Maximum
Entropy Principle for the open system, is obtained by partial maximization of
Gibbs-Shannon entropy of the closed universe over the microstate probability
distributions of the heat bath. Thus, microcanonical origin of the Entropy
Maximization procedure for an open system, is established in a rigorous manner,
showing the equivalence between apparently two distinct approaches for deriving
the Boltzmann distribution. By extending the mathematical formalism to
dynamical paths, the result may also provide an alternative justification for
the principle of path entropy maximization as well.Comment: 12 pages, no figur

### A link between the maximum entropy approach and the variational entropy form

The maximum entropy approach operating with quite general entropy measure and
constraint is considered. It is demonstrated that for a conditional or
parametrized probability distribution $f(x|\mu)$ there is a "universal"
relation among the entropy rate and the functions appearing in the constraint.
It is shown that the recently proposed variational formulation of the entropic
functional can be obtained as a consequence of this relation, that is from the
maximum entropy principle. This resolves certain puzzling points appeared in
the variational approach

### Generalized molecular chaos hypothesis and H-theorem: Problem of constraints and amendment of nonextensive statistical mechanics

Quite unexpectedly, kinetic theory is found to specify the correct definition
of average value to be employed in nonextensive statistical mechanics. It is
shown that the normal average is consistent with the generalized
Stosszahlansatz (i.e., molecular chaos hypothesis) and the associated
H-theorem, whereas the q-average widely used in the relevant literature is not.
In the course of the analysis, the distributions with finite cut-off factors
are rigorously treated. Accordingly, the formulation of nonextensive
statistical mechanics is amended based on the normal average. In addition, the
Shore-Johnson theorem, which supports the use of the q-average, is carefully
reexamined, and it is found that one of the axioms may not be appropriate for
systems to be treated within the framework of nonextensive statistical
mechanics.Comment: 22 pages, no figures. Accepted for publication in Phys. Rev.

### Selective Control of the Symmetric Dicke Subspace in Trapped Ions

We propose a method of manipulating selectively the symmetric Dicke subspace
in the internal degrees of freedom of N trapped ions. We show that the direct
access to ionic-motional subspaces, based on a suitable tuning of
motion-dependent AC Stark shifts, induces a two-level dynamics involving
previously selected ionic Dicke states. In this manner, it is possible to
produce, sequentially and unitarily, ionic Dicke states with increasing
excitation number. Moreover, we propose a probabilistic technique to produce
directly any ionic Dicke state assuming suitable initial conditions.Comment: 5 pages and 1 figure. New version with minor changes and added
references. Accepted in Physical Review

### Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations

We compare the Infrared Dirac-Born-Infeld (IR DBI) brane inflation model to
observations using a Bayesian analysis. The current data cannot distinguish it
from the \LambdaCDM model, but is able to give interesting constraints on
various microscopic parameters including the mass of the brane moduli
potential, the fundamental string scale, the charge or warp factor of throats,
and the number of the mobile branes. We quantify some distinctive testable
predictions with stringy signatures, such as the large non-Gaussianity, and the
large, but regional, running of the spectral index. These results illustrate
how we may be able to probe aspects of string theory using cosmological
observations.Comment: 54 pages, 13 figures. v2: non-Gaussianity constraint has been applied
to the model; parameter constraints have tightened significantly, conclusions
unchanged. References added; v3, minor revision, PRD versio

### Rules for transition rates in nonequilibrium steady states

Just as transition rates in a canonical ensemble must respect the principle
of detailed balance, constraints exist on transition rates in driven steady
states. I derive those constraints, by maximum information-entropy inference,
and apply them to the steady states of driven diffusion and a sheared lattice
fluid. The resulting ensemble can potentially explain nonequilibrium phase
behaviour and, for steady shear, gives rise to stress-mediated long-range
interactions.Comment: 4 pages. To appear in Physical Review Letter

### Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by
focusing on the source coding theorem. The nonadditive information content we
adopted is consistent with the concept of the form invariance structure of the
nonextensive entropy. Some general properties of the nonadditive information
entropy are studied, in addition, the relation between the nonadditivity $q$
and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev.
E(an error in proof of theorem 1 was corrected, typos corrected

### Incomplete quantum process tomography and principle of maximal entropy

The main goal of this paper is to extend and apply the principle of maximum
entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define
a so-called process entropy function being the von Neumann entropy of the state
associated with the quantum process via Choi-Jamiolkowski isomorphism. It will
be shown that an arbitrary process estimation experiment can be reformulated in
a unified framework and MaxEnt principle can be consistently exploited. We will
argue that the suggested choice for the process entropy satisfies natural list
of properties and it reduces to the state MaxEnt principle, if applied to
preparator devices.Comment: 8 pages, comments welcome, references adde

### Properties of a non-equilibrium heat bath

At equilibrium, a fluid element, within a larger heat bath, receives random
impulses from the bath. Those impulses, which induce stochastic transitions in
the system (the fluid element), respect the principle of detailed balance,
because the bath is also at equilibrium. Under continuous shear, the fluid
element adopts a non-equilibrium steady state. Because the surrounding bath of
fluid under shear is also in a non-equilibrium steady state, the system
receives stochastic impulses with a non-equilibrium distribution. Those
impulses no longer respect detailed balance, but are nevertheless constrained
by rules. The rules in question, which are applicable to a wide sub-class of
driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett.
{\bf 92}, 150601 (2004); J. Phys. A: Math. Gen. {\bf 38}, 293 (2005)] using
information-theoretic arguments. In the present paper, we provide a more
fundamental derivation, based on the uncontroversial, non-Bayesian
interpretation of probabilities as simple ratios of countable quantities. We
apply the results to some simple models of interacting particles, to
investigate the nature of forces that are mediated by a non-equilibrium
noise-source such as a fluid under shear.Comment: 14 pages, 7 figure

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