Related papers: Operator reflection positivity inequalities and th…
This paper studies the variation diminishing property of $k$-positive linear time-invariant (LTI) systems, which map inputs with $k-1$ sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz…
In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables corresponding to space-like separated parties are just…
A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski…
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…
Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a one-dimensional attractor, which must be a limit cycle in the absence of…
Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
This is a continuation of our previous paper. We consider a certain order-like relation for positive operators on a Hilbert space. This relation is defined by using the Jensen inequality with respect to the square-root function. We show…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…
We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing…
We discuss a scheme for simulating the real time quantum quench dynamics of interacting quantum spin systems within the positive-P formalism. As model systems we study the transverse field Ising model as well as the Heisenberg model…
We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of effect of dissipation on systems with time reversal invariance. We consider the nearest neighbor spacing distribution and spacing ratio to…
Several recent experiments in atomic, molecular and optical systems motivated a huge interest in the study of quantum long-range %spin systems. Our goal in this paper is to present a general description of their critical behavior and…
A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped…
The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator…
In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We…
We show that the long-time limit of the two-point correlation function obtained via the standard quantum regression theorem, a standard tool to compute correlation functions in open quantum systems, does not respect the…
We present an approach of the kicked rotor quantum resonances in position-space, based on its analogy with the optical Talbot effect. This approach leads to a very simple picture of the physical mechanism underlying the dynamics and to…
We theoretically investigate reflection and transmission measurements of two-photon and four-photon Kerr parametric oscillators (KPOs), introducing interference effects between inter-level transitions. Due to the level degeneracy of a KPO,…