Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLarge deviations and Chernoff bound for certain correlated states on a spin chain
139
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we extend the results of Lenci and Rey-Bellet on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state, in the setting of translation-invariant finite-range interactions. We show that a certain factorization property of the reference state is sufficient for a large deviation upper bound to hold and that this factorization property is satisfied by Gibbs states of the above kind as well as finitely correlated states. As an application of the methods the Chernoff bound for correlated states with factorization property is studied. In the specific case of the distributions of the ergodic averages of a one-site observable with respect to an ergodic finitely correlated state the spectral theory of positive maps is applied to prove the full large deviation principle.
rate research
Read More
We construct explicit bound state wave functions and bound state energies for certain $N$--body Hamiltonians in one dimension that are analogous to $N$--electron Hamiltonians for (three-dimensional) atoms and monatomic ions.
We study the entropy of pure shift-invariant states on a quantum spin chain. Unlike the classical case, the local restrictions to intervals of length $N$ are typically mixed and have therefore a non-zero entropy $S_N$ which is, moreover, monotonically increasing in $N$. We are interested in the asymptotics of the total entropy. We investigate in detail a class of states derived from quasi-free states on a CAR algebra. These are characterised by a measurable subset of the unit interval. As the entropy density is known to vanishes, $S_N$ is sublinear in $N$. For states corresponding to unions of finitely many intervals, $S_N$ is shown to grow slower than $(log N)^2$. Numerical calculations suggest a $log N$ behaviour. For the case with infinitely many intervals, we present a class of states for which the entropy $S_N$ increases as $N^alpha$ where $alpha$ can take any value in $(0,1)$.
We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via $L log L$ gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.
In this paper we provide a detailed description of the eigenvalue $ E_{D}(x_0)leq 0$ (respectively $ E_{N}(x_0)leq 0$) of the self-adjoint Hamiltonian operator representing the negative Laplacian on the positive half-line with a Dirichlet (resp. Neuman) boundary condition at the origin perturbed by an attractive Dirac distribution $-lambda delta(x-x_0)$ for any fixed value of the magnitude of the coupling constant. We also investigate the $lambda$-dependence of both eigenvalues for any fixed value of $x_0$. Furthermore, we show that both systems exhibit resonances as poles of the analytic continuation of the resolvent. These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverios monograph, perturbed by an attractive $delta$-distribution supported on the spherical shell of radius $r_0$.
Generalized Large deviation principles was developed for Colombeau-Ito SDE with a random coefficients. We is significantly expand the classical theory of large deviations for randomly perturbed dynamical systems developed by Freidlin and Wentzell.Using SLDP approach, jumps phenomena, in financial markets, also is considered. Jumps phenomena, in financial markets is explained from the first principles, without any reference to Poisson jump process. In contrast with a phenomenological approach we explain such jumps phenomena from the first principles, without any reference to Poisson jump process.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
