相关论文: A Meta Logarithmic-Sobolev Inequality for Phase-Co…

We prove that every probability measure $\mu$ satisfying the stationary Fokker-Planck-Kolmogorov equation obtained by a $\mu$-integrable perturbation $v$ of the drift term $-x$ of the Ornstein-Uhlenbeck operator is absolutely continuous…

Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N)…

A quantum analogue of the Central Limit Theorem (CLT) for bosonic system, first introduced by Cushen and Hudson (1971), states that the $n$-fold convolution $\rho^{\boxplus n}$ of an $m$-mode quantum state $\rho$, with zero first moments…

We establish a Leray- Trudinger Type inequality in the anisotropic setting induced by a strongly convex Finsler norm F. The result generalizes classical exponential integrability inequalities for Sobolev functions to the framework of…

Log-Sobolev inequalities (LSIs) upper-bound entropy via a multiple of the Dirichlet form (i.e. norm of a gradient). In this paper we prove a family of entropy-energy inequalities for the binary hypercube which provide a non-linear…

Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of…

We develop an inhomogeneous quantum mean-field approach to the behavior of collective excitations across the superfluid-Mott glass quantum phase transition in two dimensions, complementing recent quantum Monte Carlo simulations [Phys. Rev.…

We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show that this approach leads to improvement of Wu's inequality…

In this work, we obtain an existence of nontrivial solutions to a minimization problem involving a fractional Hardy-Sobolev type inequality in the case of inner singularity. Precisely, for $\lambda>0$ we analyze the attainability of the…

For general ferromagnetic Ising models whose coupling matrix has bounded spectral radius, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the model. This bound implies very…

On a doubling metric measure space $(M,d,\mu)$ endowed with a "carr\'e du champ", let $\mathcal{L}$ be the associated Markov generator and $\dot L^{p}_\alpha(M,\mathcal{L},\mu)$ the corresponding homogeneous Sobolev space of order…

This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…

The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…

We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite…

The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the…

A new method is proposed for the calculation of full density matrix and thermodynamic functions of a many-boson system. Explicit expressions are obtained in the pair correlations approximation for an arbitrary temperature. The theory is…

We derive families of optimal and near-optimal probe states for quantum estimation of the coupling constants of a general two-mode number-conserving bosonic Hamiltonian describing one-body and two-body dynamics. We find that the optimal…

We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…

We identify sharp spaces and prove quantitative and non-quantitative stability results for the logarithmic Sobolev inequality involving Wasserstein and $L^p$ metrics. The techniques are based on optimal transport theory and Fourier…

In this article, we study the mean field limit of weakly interacting diffusions for confining and interaction potentials that are not necessarily convex. We explore the relationship between the large $N$ limit of the constant in the…