Related papers: On local quantum Gibbs states
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant…
We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this…
We investigate the entropy bound for local quantum field theory in this paper. Both the bosonic and fermionic fields confined to an asymptotically flat spacetime are examined. By imposing the non-gravitational collapse condition, we find…
The study is motivated by the known fact that, in the noncompact case, the main minimum-problem of the theory of interior capacities of condensers in a locally compact space is in general unsolvable, and this occurs even under very natural…
For the well-known model of a system of N particles with interaction (N-body problem), we consider the spatial problem of finding the minimum of the function of the kinetic energy of a system on its phase space under conditions on its size…
We investigate the existence of local minimizers with prescribed $L^2$-norm for the energy functional associated to the mass-supercritical nonlinear Schr\"{o}dinger equation on the product space $\mathbb{R}^N \times M^k$, where $(M^k,g)$ is…
We study when local reduced density operators, viewed as quantum marginals, can be assembled into a global quantum state with a prescribed Markov structure. The starting point is a canonical logarithmic construction $T(\mathcal R)$, the…
We consider vectorial problems in the calculus of variations with an additional pointwise constraint. Our admissible mappings ${\bf n}:\mathbb{R}^k\rightarrow \mathbb{R}^d$ satisfy ${\bf n}(x)\in M$, where $M$ is a manifold embedded in…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, a law of large numbers is shown to hold in a…
We study finite-difference approximations of both Poisson and Poisson-Boltzmann (PB) electrostatic energy functionals for periodic structures constrained by Gauss' law and a class of local algorithms for minimizing the finite-difference…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…