602 research outputs found
Time-reversal symmetric resolution of unity without background integrals in open quantum systems
We present a new complete set of states for a class of open quantum systems,
to be used in expansion of the Green's function and the time-evolution
operator. A remarkable feature of the complete set is that it observes
time-reversal symmetry in the sense that it contains decaying states (resonant
states) and growing states (anti-resonant states) parallelly. We can thereby
pinpoint the occurrence of the breaking of time-reversal symmetry at the choice
of whether we solve Schroedinger equation as an initial-condition problem or a
terminal-condition problem. Another feature of the complete set is that in the
subspace of the central scattering area of the system, it consists of
contributions of all states with point spectra but does not contain any
background integrals. In computing the time evolution, we can clearly see
contribution of which point spectrum produces which time dependence. In the
whole infinite state space, the complete set does contain an integral but it is
over unperturbed eigenstates of the environmental area of the system and hence
can be calculated analytically. We demonstrate the usefulness of the complete
set by computing explicitly the survival probability and the escaping
probability as well as the dynamics of wave packets. The origin of each term of
matrix elements is clear in our formulation, particularly the exponential
decays due to the resonance poles.Comment: 62 pages, 13 figure
Non-trivial stably free modules over crossed products
We consider the class of crossed products of noetherian domains with
universal enveloping algebras of Lie algebras. For algebras from this class we
give a sufficient condition for the existence of projective non-free modules.
This class includes Weyl algebras and universal envelopings of Lie algebras,
for which this question, known as noncommutative Serre's problem, was
extensively studied before. It turns out that the method of lifting of
non-trivial stably free modules from simple Ore extensions can be applied to
crossed products after an appropriate choice of filtration. The motivating
examples of crossed products are provided by the class of RIT algebras,
originating in non-equilibrium physics.Comment: 13 page
Stable States of Biological Organisms
A novel model of biological organisms is advanced, treating an organism as a
self-consistent system subject to a pathogen flux. The principal novelty of the
model is that it describes not some parts, but a biological organism as a
whole. The organism is modeled by a five-dimensional dynamical system. The
organism homeostasis is described by the evolution equations for five
interacting components: healthy cells, ill cells, innate immune cells, specific
immune cells, and pathogens. The stability analysis demonstrates that, in a
wide domain of the parameter space, the system exhibits robust structural
stability. There always exist four stable stationary solutions characterizing
four qualitatively differing states of the organism: alive state, boundary
state, critical state, and dead state.Comment: Latex file, 12 pages, 4 figure
Hidden Markov Model Variants and their Application
Markov statistical methods may make it possible to develop an unsupervised learning process that can automatically identify genomic structure in prokaryotes in a comprehensive way. This approach is based on mutual information, probabilistic measures, hidden Markov models, and other purely statistical inputs. This approach also provides a uniquely common ground for comparative prokaryotic genomics. The approach is an on-going effort by its nature, as a multi-pass learning process, where each round is more informed than the last, and thereby allows a shift to the more powerful methods available for supervised learning at each iteration. It is envisaged that this "bootstrap" learning process will also be useful as a knowledge discovery tool. For such an ab initio prokaryotic gene-finder to work, however, it needs a mechanism to identify critical motif structure, such as those around the start of coding or start of transcription (and then, hopefully more). For eukaryotes, even with better start-of-coding identification, parsing of eukaryotic coding regions by the HMM is still limited by the HMM's single gene assumption, as evidenced by the poor performance in alternatively spliced regions. To address these complications an approach is described to expand the states in a eukaryotic gene-predictor HMM, to operate with two layers of DNA parsing. This extension from the single layer gene prediction parse is indicated after preliminary analysis of the C. elegans alt-splice statistics. State profiles have made use of a novel hash-interpolating MM (hIMM) method. A new implementation for an HMM-with-Duration is also described, with far-reaching application to gene-structure identification and analysis of channel current blockade data
Oscillatory behaviour in a lattice prey-predator system
Using Monte Carlo simulations we study a lattice model of a prey-predator
system. We show that in the three-dimensional model populations of preys and
predators exhibit coherent periodic oscillations but such a behaviour is absent
in lower-dimensional models. Finite-size analysis indicate that amplitude of
these oscillations is finite even in the thermodynamic limit. In our opinion,
this is the first example of a microscopic model with stochastic dynamics which
exhibits oscillatory behaviour without any external driving force. We suggest
that oscillations in our model are induced by some kind of stochastic
resonance.Comment: 7 pages, 10 figures, Phys.Rev.E (Nov. 1999
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604.
Discussion expanded to include the case of Hamiltonians with an infinitely
degenerate spectru
Kinetics of Clustering in Traffic Flows
We study a simple aggregation model that mimics the clustering of traffic on
a one-lane roadway. In this model, each ``car'' moves ballistically at its
initial velocity until it overtakes the preceding car or cluster. After this
encounter, the incident car assumes the velocity of the cluster which it has
just joined. The properties of the initial distribution of velocities in the
small velocity limit control the long-time properties of the aggregation
process. For an initial velocity distribution with a power-law tail at small
velocities, \pvim as , a simple scaling argument shows that the
average cluster size grows as n \sim t^{\va} and that the average velocity
decays as v \sim t^{-\vb} as . We derive an analytical solution
for the survival probability of a single car and an asymptotically exact
expression for the joint mass-velocity distribution function. We also consider
the properties of spatially heterogeneous traffic and the kinetics of traffic
clustering in the presence of an input of cars.Comment: 18 pages, Plain TeX, 2 postscript figure
Modeling and Simulation of Multi-Lane Traffic Flow
A most important aspect in the field of traffic modeling is the simulation of
bottleneck situations. For their realistic description a macroscopic multi-lane
model for uni-directional freeways including acceleration, deceleration,
velocity fluctuations, overtaking and lane-changing maneuvers is systematically
deduced from a gas-kinetic (Boltzmann-like) approach. The resulting equations
contain corrections with respect to previous models. For efficient computer
simulations, a reduced model delineating the coarse-grained temporal behavior
is derived and applied to bottleneck situations.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
An Alternative Interpretation of Statistical Mechanics
In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics
A linear nonequilibrium thermodynamics approach to optimization of thermoelectric devices
Improvement of thermoelectric systems in terms of performance and range of
applications relies on progress in materials science and optimization of device
operation. In this chapter, we focuse on optimization by taking into account
the interaction of the system with its environment. For this purpose, we
consider the illustrative case of a thermoelectric generator coupled to two
temperature baths via heat exchangers characterized by a thermal resistance,
and we analyze its working conditions. Our main message is that both electrical
and thermal impedance matching conditions must be met for optimal device
performance. Our analysis is fundamentally based on linear nonequilibrium
thermodynamics using the force-flux formalism. An outlook on mesoscopic systems
is also given.Comment: Chapter 14 in "Thermoelectric Nanomaterials", Editors Kunihito
Koumoto and Takao Mori, Springer Series in Materials Science Volume 182
(2013
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