118 research outputs found
An alternative to the conventional micro-canonical ensemble
Usual approach to the foundations of quantum statistical physics is based on
conventional micro-canonical ensemble as a starting point for deriving
Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual
and practical questions unanswered. Here we discuss these questions, thereby
motivating the study of a natural alternative known as Quantum Micro-Canonical
(QMC) ensemble. We present a detailed numerical study of the properties of the
QMC ensemble for finite quantum systems revealing a good agreement with the
existing analytical results for large quantum systems. We also propose the way
to introduce analytical corrections accounting for finite-size effects. With
the above corrections, the agreement between the analytical and the numerical
results becomes very accurate. The QMC ensemble leads to an unconventional kind
of equilibrium, which may be realizable after strong perturbations in small
isolated quantum systems having large number of levels. We demonstrate that the
variance of energy fluctuations can be used to discriminate the QMC equilibrium
from the BG equilibrium. We further suggest that the reason, why BG equilibrium
commonly occurs in nature rather than the QMC-type equilibrium, has something
to do with the notion of quantum collapse.Comment: 25 pages, 6 figure
PT-symmetry breaking in complex nonlinear wave equations and their deformations
We investigate complex versions of the Korteweg-deVries equations and an Ito
type nonlinear system with two coupled nonlinear fields. We systematically
construct rational, trigonometric/hyperbolic, elliptic and soliton solutions
for these models and focus in particular on physically feasible systems, that
is those with real energies. The reality of the energy is usually attributed to
different realisations of an antilinear symmetry, as for instance PT-symmetry.
It is shown that the symmetry can be spontaneously broken in two alternative
ways either by specific choices of the domain or by manipulating the parameters
in the solutions of the model, thus leading to complex energies. Surprisingly
the reality of the energies can be regained in some cases by a further breaking
of the symmetry on the level of the Hamiltonian. In many examples some of the
fixed points in the complex solution for the field undergo a Hopf bifurcation
in the PT-symmetry breaking process. By employing several different variants of
the symmetries we propose many classes of new invariant extensions of these
models and study their properties. The reduction of some of these models yields
complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv
policy; higher resolutions maybe obtained from the authors upon request
Complexified dynamical systems.
Accepted versio
Complex trajectories of a simple pendulum
Accepted versio
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Exact quantization of a PT-symmetric (reversible) Li\'enard-type nonlinear oscillator
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard
type one dimensional nonlinear oscillator both semiclassically and quantum
mechanically. The associated time independent classical Hamiltonian is of
non-standard type and is invariant under a combined coordinate reflection and
time reversal transformation. We use von Roos symmetric ordering procedure to
write down the appropriate quantum Hamiltonian. While the quantum problem
cannot be tackled in coordinate space, we show how the problem can be
successfully solved in momentum space by solving the underlying Schr\"{o}dinger
equation therein. We obtain explicitly the eigenvalues and eigenfunctions (in
momentum space) and deduce the remarkable result that the spectrum agrees
exactly with that of the linear harmonic oscillator, which is also confirmed by
a semiclassical modified Bohr-Sommerfeld quantization rule, while the
eigenfunctions are completely different.Comment: 10 pages, 1 figure, Fast Track Communicatio
A generalized quantum microcanonical ensemble
We discuss a generalized quantum microcanonical ensemble. It describes
isolated systems that are not necessarily in an eigenstate of the Hamilton
operator. Statistical averages are obtained by a combination of a time average
and a maximum entropy argument to resolve the lack of knowledge about initial
conditions. As a result, statistical averages of linear observables coincide
with values obtained in the canonical ensemble. Non-canonical averages can be
obtained by taking into account conserved quantities which are non-linear
functions of the microstate.Comment: improved version, new titl
Exact Isospectral Pairs of PT-Symmetric Hamiltonians
A technique for constructing an infinite tower of pairs of PT-symmetric
Hamiltonians, and (n=2,3,4,...), that have exactly the
same eigenvalues is described. The eigenvalue problem for the first Hamiltonian
of the pair must be posed in the complex domain, so its
eigenfunctions satisfy a complex differential equation and fulfill homogeneous
boundary conditions in Stokes' wedges in the complex plane. The eigenfunctions
of the second Hamiltonian of the pair obey a real differential
equation and satisfy boundary conditions on the real axis. This equivalence
constitutes a proof that the eigenvalues of both Hamiltonians are real.
Although the eigenvalue differential equation associated with is
real, the Hamiltonian exhibits quantum anomalies (terms
proportional to powers of ). These anomalies are remnants of the complex
nature of the equivalent Hamiltonian . In the classical limit in
which the anomaly terms in are discarded, the pair of Hamiltonians
and have closed classical orbits whose
periods are identical.Comment: 18 pages, 12 figure
First-Year Spectroscopy for the SDSS-II Supernova Survey
This paper presents spectroscopy of supernovae discovered in the first season
of the Sloan Digital Sky Survey-II Supernova Survey. This program searches for
and measures multi-band light curves of supernovae in the redshift range z =
0.05 - 0.4, complementing existing surveys at lower and higher redshifts. Our
goal is to better characterize the supernova population, with a particular
focus on SNe Ia, improving their utility as cosmological distance indicators
and as probes of dark energy. Our supernova spectroscopy program features
rapid-response observations using telescopes of a range of apertures, and
provides confirmation of the supernova and host-galaxy types as well as precise
redshifts. We describe here the target identification and prioritization, data
reduction, redshift measurement, and classification of 129 SNe Ia, 16
spectroscopically probable SNe Ia, 7 SNe Ib/c, and 11 SNe II from the first
season. We also describe our efforts to measure and remove the substantial host
galaxy contamination existing in the majority of our SN spectra.Comment: Accepted for publication in The Astronomical Journal(47pages, 9
figures
Euclid preparation: XIII. Forecasts for galaxy morphology with the Euclid Survey using deep generative models
We present a machine learning framework to simulate realistic galaxies for the Euclid Survey, producing more complex and realistic galaxies than the analytical simulations currently used in Euclid. The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real Hubble Space Telescope observations by deep generative models. We simulate a galaxy field of 0.4 deg2 as it will be seen by the Euclid visible imager VIS, and we show that galaxy structural parameters are recovered to an accuracy similar to that for pure analytic Sérsic profiles. Based on these simulations, we estimate that the Euclid Wide Survey (EWS) will be able to resolve the internal morphological structure of galaxies down to a surface brightness of 22.5 mag arcsec-2, and the Euclid Deep Survey (EDS) down to 24.9 mag arcsec-2. This corresponds to approximately 250 million galaxies at the end of the mission and a 50% complete sample for stellar masses above 1010.6 M (resp. 109.6 M) at a redshift z ∼ 0.5 for the EWS (resp. EDS). The approach presented in this work can contribute to improving the preparation of future high-precision cosmological imaging surveys by allowing simulations to incorporate more realistic galaxies
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