相关论文: Escort density operators and generalized quantum i…
We define an infinite dimensional modification of lower-semicomputability of density operators by G\'acs with an attempt to fix some problem in the paper. Our attempt is partly achieved by showing the existence of universal operator under…
The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is…
A definable set $X$ in the first-order language of rings defines a family of random vectors: for each finite field $\mathbb{F}_q$, let the distribution be supported and uniform on the $\mathbb{F}_q$-rational points of $X$. We employ results…
We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic,…
We consider a family of integral operators which appears when analyzing layered equilibria and front dynamics of a phase kinetics equation with a conservation law. We study the spectra of these operators in $L^2$ and derive a lower bound…
A novel method to determine the density and temperature of a system based on quantum Fermionic fluctuations is generalized to the limit where the reached temperature T is large compared to the Fermi energy {\epsilon}f . Quadrupole and…
By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the Parametric Representation with Environmental Coherent States) we derive an equation of motion for the reduced density operator of an…
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…
In Partially Observable Markov Decision Processes (POMDPs), maintaining and updating belief distributions over possible underlying states provides a principled way to summarize action-observation history for effective decision-making under…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second…
We consider families of finite quantum graphs of increasing size and we are interested in how eigenfunctions are distributed over the graph. As a measure for the distribution of an eigenfunction on a graph we introduce the entropy, it has…
Exponential families form the backbone of modern statistics and machine learning, but textbooks seldom derive them from first principles in an accessible way. Although minimal sufficiency and the principle of maximum entropy, originating in…
Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square, in which both bandwidth and received signal power can be limited significantly. A narrow-band model is assumed where the…
Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…