相关论文: L'Hopital-Type Rules for Monotonicity with Applica…
The problem of studying the quantum Hall effect on manifolds with nonconstant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when…
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus…
We introduce an approach to scattering problems in theories with non-Hermitian Hamiltonian, usually known as PT-symmetric quantum theories, by means of the adiabatic switching of the interaction. The modifications of usual methods needed to…
We study the expansion of the universe at late times in the case that the cosmological constant obeys certain scaling laws motivated by renormalisation group running in quantum theories. The renormalisation scale is identified with the…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
In this paper, we discuss the compatibility between the rotating-wave and the adiabatic approximations for controlled quantum systems. Although the paper focuses on applications to two-level quantum systems, the main results apply in higher…
We provide a brief discussion regarding relativistic limits on the discretization and temporal resolution of time values in a quantum clock. Our clock is characterized by a time observable chosen to be the complement of a bounded and…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum…
The positivity conditions of the relative entropy between two thermal equilibrium states $\hat{\rho}_1$ and $\hat{\rho}_2$ are used to obtain upper and lower bounds for the subtraction of their entropies, the Helmholtz potential and the…
In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…
In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, several complete monotonicity of functions involving ratios of two gamma or $q$-gamma…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…