28,327 research outputs found
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 -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
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
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
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
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