A semiclassical theory of quantum noise in open chaotic systems

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica

Superconductivity and Dirac Fermions in 112-phase Pnictides

This article reviews the status of current research on the 112-phase of pnictides. The 112-phase has gained augmented attention due to the recent discovery of high-temperature superconductivity in \cl with a maximum critical temperature \tc\sim 47\,K upon Sb substitution. The structural, magnetic, and electronic properties of \cl bear some similarities with other superconducting pnictide phases, however, the different valence states of the pnictogen and the presence of a metallic spacer layer are unique features of the 112-system. Low-temperature superconductivity which coexists with antiferromagnetic order was observed in transition metal (Ni, Pd) deficient 112-compounds like \cn, \lpb, \lps, \lns. Besides superconductivity, the presence of naturally occurring anisotropic Dirac Fermionic states were observed in the layered 112-compounds \smb, \cmb, \lab which are of significant interest for future nanoelectronics as an alternative to graphene. In these compounds, the linear energy dispersion resulted in a high magnetoresistance that stayed unsaturated even at the highest applied magnetic fields. Here, we describe various 112-type materials systems combining experimental results and theoretical predictions to stimulate further research on this less well-known member of the pnictide family.Comment: 18 pages, 20 figure

Comments on the size of the simulation box in cosmological N-Body simulations

N-Body simulations are a very important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of high redshift universe and comparison with observations would not have been possible without N-Body simulations. Given the importance of this tool, it is essential to understand its limitations as ignoring the limitations can easily lead to interesting but unreliable results. In this paper we study the limitations arising out of the finite size of simulation volume. This finite size implies that modes larger than the size of the simulation volume are ignored and a truncated power spectrum is simulated. If the simulation volume is large enough then the mass in collapsed haloes expected from the full power spectrum and from the truncated power spectrum should match. We propose a quantitative measure based on this approach that allows us to compute the minimum box size for an N-Body simulation. We find that the required box size for simulations of LCDM model at high redshifts is much larger than is typically used. We can also use this approach to quantify the effect of perturbations at large scales for power law models and we find that if we fix the scale of non-linearity, the required box size becomes very large as the index becomes small. The appropriate box size computed using this approach is also an appropriate choice for the transition scale when tools like MAP (Tormen and Bertschinger, 1996) that add the contribution of the missing power are used.Comment: 7 pages, 8 figures, Accepted for publication in the MNRA

Comment on "A note on the construction of the Ermakov-Lewis invariant"

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new

Birkhoff's Theorem in Higher Derivative Theories of Gravity

In this paper we present a class of higher derivative theories of gravity which admit Birkhoff's theorem. In particular, we explicitly show that in this class of theories, although generically the field equations are of fourth order, under spherical (plane or hyperbolic) symmetry, all the field equations reduce to second order and have exactly the same or similar structure to those of Lovelock theories, depending on the spacetime dimensions and the order of the Lagrangian.Comment: 7 pages, no figures. v1: This version received an Honorable Mention from the Gravity Research Foundation - 2011 Awards for Essays on Gravitation. v2: Expanded version. To appear in CQ