6,484 research outputs found
Entropy production in open quantum systems: exactly solvable qubit models
We present analytical results for the time-dependent information entropy in
exactly solvable two-state (qubit) models. The first model describes dephasing
(decoherence) in a qubit coupled to a bath of harmonic oscillators. The entropy
production for this model in the regimes of "complete" and "incomplete"
decoherence is discussed. As another example, we consider the damped
Jaynes-Cummings model describing a spontaneous decay of a two-level system into
the field vacuum. It is shown that, for all strengths of coupling, the open
system passes through the mixed state with the maximum information entropy.Comment: 9 pages, 3 figure
New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
Integrable N-particle systems have an important property that the associated
Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not
apply to the most interesting class of elliptic and double-elliptic systems.
Studying the commutativity conjecture for theta-functions on the families of
associated spectral curves, we derive some other non-linear equations for the
perturbative Seiberg-Witten prepotential, which turn out to have exactly the
double-elliptic system as their generic solution. In contrast with the WDVV
equations, the new equations acquire non-perturbative corrections which are
straightforwardly deducible from the commutativity conditions. We obtain such
corrections in the first non-trivial case of N=3 and describe the structure of
non-perturbative solutions as expansions in powers of the flat moduli with
coefficients that are (quasi)modular forms of the elliptic parameter.Comment: 25 page
Unitary matrix integrals in the framework of Generalized Kontsevich Model. I. Brezin-Gross-Witten Model
We advocate a new approach to the study of unitary matrix models in external
fields which emphasizes their relationship to Generalized Kontsevich Models
(GKM) with non-polynomial potentials. For example, we show that the partition
function of the Brezin-Gross-Witten Model (BGWM), which is defined as an
integral over unitary matrices, , can also be considered as a GKM with potential . Moreover, it can be interpreted as the generating functional for
correlators in the Penner model. The strong and weak coupling phases of the
BGWM are identified with the "character" (weak coupling) and "Kontsevich"
(strong coupling) phases of the GKM, respectively. This sort of GKM deserves
classification as one (i.e. or ) when in the Kontsevich
phase. This approach allows us to further identify the
Harish-Chandra-Itzykson-Zuber (IZ) integral with a peculiar GKM, which arises
in the study of theory and, further, with a conventional 2-matrix model
which is rewritten in Miwa coordinates. Inspired by the considered unitary
matrix models, some further extensions of the GKM treatment which are inspired
by the unitary matrix models which we have considered are also developed. In
particular, as a by-product, a new simple method of fixing the Ward identities
for matrix models in an external field is presented.Comment: FIAN/TD-16/93, ITEP-M6/93, UBC/S-93/93 (39 pages
Phase behaviour of block copolymer melts with arbitrary architecture
The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for
microphase separation in AB block copolymer melts is generalized for systems
with arbitrary topology of molecules. A diagrammatic technique for calculation
of the monomeric correlation functions is developed. The free energies of
various mesophases are calculated within the second-harmonic approximation.
Model highly-branched tree-like structures are considered as an example and
their phase diagrams are obtained. The topology of molecules is found to
influence the spinodal temperature and asymmetry of the phase diagrams, but not
the types of phases and their order. We suggest that all model AB
block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also
http://rugmd4.chem.rug.nl/~morozov/research.htm
Short time dynamics with initial correlations
The short-time dynamics of correlated systems is strongly influenced by
initial correlations giving rise to an additional collision integral in the
non-Markovian kinetic equation. Exact cancellation of the two integrals is
found if the initial state is thermal equilibrium which is an important
consistency criterion. Analytical results are given for the time evolution of
the correlation energy which are confirmed by comparisons with molecular
dynamics simulations (MD)
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