Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,\lambda,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta = \hbar^{\alpha}\lambda^{\beta}D^{\gamma}$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.Comment: Submitte

Structure of electromagnetic fields in spatially dispersive media of arbitrary geometry

The nature of the electromagnetic field in a spatially dispersive medium, occupying an arbitrary domain V is investigated, under conditions when spatial dispersion effects arise from the presence of an isolated exciton transition band. It is shown that the electric field at frequency ω close to the exciton transition frequency may, in general, be expressed in the form E→ (r→,ω)=E→t(1) (r→, ω)+E→t(2)(r→, ω)+E→l(r→, ω), where E→t(j)(r→, ω)(j=1, 2) are transverse fields and E→l(r→, ω) is a longitudinal field; and that each of these three fields satisfies a Helmholtz equation. The wave numbers occurring in the three Helmholtz equations are the roots of the dispersion relations appropriate to the medium. It is further shown that the three fields are coupled by a linear relation, which is shown to imply a recently derived nonlocal boundary condition on the nonlocal polarization, expressed in the form of an extinction theorem. These results are generalizations of certain results obtained not long ago by Sein, Birman and Sein, Agarwal, Pattanayak, and Wolf, and Maradudin and Mills

Trajectory versus probability density entropy

We study the problem of entropy increase of the Bernoulli-shift map without recourse to the concept of trajectory and we discuss whether, and under which conditions if it does, the distribution density entropy coincides with the Kolmogorov-Sinai entropy, namely, with the trajectory entropy.Comment: 24 page

The progestin receptor interactome in the female mouse hypothalamus: Interactions with synaptic proteins are isoform specific and ligand dependent

Progestins bind to the progestin receptor (PR) isoforms, PR-A and PR-B, in brain to influence development, female reproduction, anxiety, and stress. Hormone-activated PRs associate with multiple proteins to form functional complexes. In the present study, proteins from female mouse hypothalamus that associate with PR were isolated using affinity pull-down assays with glutathione S-transferase–tagged mouse PR-A and PR-B. Using complementary proteomics approaches, reverse phase protein array (RPPA) and mass spectrometry, we identified hypothalamic proteins that interact with PR in a ligand-dependent and isoform-specific manner and were confirmed by Western blot. Synaptic proteins, including synapsin-I and synapsin-II, interacted with agonist-bound PR isoforms, suggesting that both isoforms function in synaptic plasticity. In further support, synaptogyrin-III and synapsin-III associated with PR-A and PR-B, respectively. PR also interacted with kinases, including c-Src, mTOR, and MAPK1, confirming phosphorylation as an integral process in rapid effects of PR in the brain. Consistent with a role in transcriptional regulation, PR associated with transcription factors and coactivators in a ligand-specific and isoform-dependent manner. Interestingly, both PR isoforms associated with a key regulator of energy homeostasis, FoxO1, suggesting a novel role for PR in energy metabolism. Because many identified proteins in this PR interactome are synaptic proteins, we tested the hypothesis that progestins function in synaptic plasticity. Indeed, progesterone enhanced synaptic density, by increasing synapsin-I–positive synapses, in rat primary cortical neuronal cultures. This novel combination of RPPA and mass spectrometry allowed identification of PR action in synaptic remodeling and energy homeostasis and reveals unique roles for progestins in brain function and disease

Fluctuation-dissipation relationship in chaotic dynamics

We consider a general N-degree-of-freedom dissipative system which admits of chaotic behaviour. Based on a Fokker-Planck description associated with the dynamics we establish that the drift and the diffusion coefficients can be related through a set of stochastic parameters which characterize the steady state of the dynamical system in a way similar to fluctuation-dissipation relation in non-equilibrium statistical mechanics. The proposed relationship is verified by numerical experiments on a driven double well system.Comment: Revtex, 23 pages, 2 figure

Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities like entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.Comment: RevTex, 17 pages, 9 figures. To appear in Phys. Rev.

Experimental signatures of the quantum-classical transition in a nanomechanical oscillator modeled as a damped driven double-well problem

We demonstrate robust and reliable signatures for the transition from quantum to classical behavior in the position probability distribution of a damped double-well system using the Qunatum State Diffusion approach to open quantum systems. We argue that these signatures are within experimental reach, for example in a doubly-clamped nanomechanical beam.Comment: Proceedings of the conference FMQT 1

Ordered and periodic chaos of the bounded one dimensinal multibarrier potential

Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets result upon passing through the multibarrier potential.Comment: 16 pages, 9 figures, 1 Table. Some former text removed and other introduce

The noise properties of stochastic processes and entropy production

Based on a Fokker-Planck description of external Ornstein-Uhlenbeck noise and cross-correlated noise processes driving a dynamical system we examine the interplay of the properties of noise processes and the dissipative characteristic of the dynamical system in the steady state entropy production and flux. Our analysis is illustrated with appropriate examples.Comment: RevTex, 1 figure, To appear in Phys. Rev.