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Several results point to deep relations between noncommutative geometry and class eld theory ([3],
[10], [20], [22]). In [3] a quantum statistical mechanical system (BC) is exhibited, with partition...
An important problem in smooth ergodic theory is to understand an
appearance of chaotic behavior in systems governed by deterministic
laws. Now it is understood that chaotic behavior is caused by th...
ON DIFFERENTIABILITY OF SRB STATES FOR PARTIALLY HYPERBOLIC SYSTEMS
DIFFERENTIABILITY HYPERBOLIC SYSTEMS
2015/9/29
Consider a one parameter family of diffeomorphisms
fε such that f0 is an Anosov element in a standard abelian Anosov
action having sufficiently strong mixing properties. Let νε be any
u-...
THE DIFFUSION COEFFICIENT FOR PIECEWISE EXPANDING MAPS OF THE INTERVAL WITH METASTABLE STATES
DIFFUSION COEFFICIENT WITH METASTABLE STATES
2015/9/29
Consider a piecewise smooth expanding map of the interval possessing several
invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
Attainment of the multiple quantum Chernoff bound for certain ensembles of mixed states
multiple quantum Chernoff bound certain ensembles mixed states
2015/8/25
We consider the problem of detecting the true quantum state among r possible ones, based onmeasurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent f...
Asymptotically Optimal Discrimination between Pure Quantum States
multiple quantum state discrimination generalized quantum Chernoff distance quantum hypothesis testing error exponents
2015/8/25
We consider the decision problem between a finite numberof states of a finite quantum system, when an arbitrarily large number of copies of the system is available for measurements. We provide an uppe...
Gibbs states and the set of solutions of random constraint satisfaction problems
Gibbs random constraints the solution
2015/8/21
Gibbs states and the set of solutions of random constraint satisfaction problems.
The non-local Fisher-KPP equation:traveling waves and steady states
non-local Fisher-KPP equation traveling waves steady states
2015/7/14
We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our fir...
On the nonlocal Fisher-KPP equation:steady states,spreading speed and global bounds
nonlocal Fisher-KPP equation steady states spreading speed global bounds
2015/7/14
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions,and prove uniform upper ...
MULTIPLE MIXED STATES OF NODAL SOLUTIONS FOR NONLINEAR SCHR ODINGER SYSTEMS
MULTIPLE MIXED STATES NONLINEAR SCHR ODINGER SYSTEMS
2014/9/26
In this paper we develop a general critical point theory to deal with existence
and locations of multiple critical points produced by minimax methods in relation to mul-tiple invariant sets of the as...
Note on the Number of Steady States for a 2D Smoluchowski Equation
the Number Steady States 2D Smoluchowski Equation
2014/4/4
Dynamics of concentrated polymer solutions are modeled by a Smoluchowski equation. At high concentrations, such solutions form liquid crystalline polymers of nematic structure. We prove that at high i...
Optimal Weighting of Multi-View Data with Low Dimensional Hidden States
Low Dimensional Hidden States Optimal Weighting Multi-View Data
2012/11/23
In Natural Language Processing (NLP) tasks, data often has the following two properties: First, data can be chopped into multi-views which has been successfully used for dimension reduction purposes. ...
A Mermin--Wagner theorem for quantum Gibbs states on 2D graphs, I
quantum bosonic system with continuous spins symmetry group the Feynman–Kac representation bi-dimensional graphs Gibbs states
2012/6/25
This is the the first of a series of papers considering properties of quantum systems over 2D graphs or manifolds, with continuous spins. In the model considered here the phase space of a single spin ...
We study the nature of the Nonlinear Schr\"odinger equation ground states on the product spaces $\R^n\times M^k$, where $M^k$ is a compact Riemannian manifold. We prove that for small $L^2$ masses the...
Free evolution on algebras with two states II
Free evolution algebras two states II Operator Algebras
2012/4/17
Denote by $J$ the operator of coefficient stripping. We show that for any free convolution semigroup of measures $\nu_t$ with finite variance, applying a single stripping produces semicircular evoluti...