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This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
Value semigroups of non irreducible singular algebraic curves and their fractional ideals are submonoids of $\mathbb Z^n$ that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements.…
Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used…
We {characterize the multipartite entanglement in a quantum system by the quantity} which vanishes if only the quantum system may be decomposed into two weakly entangled subsystems, unlike measures of multipartite entanglement introduced…
Preserving entanglement is a crucial dynamical process for entanglement-based quantum computation and quantum-information processes, such as one-way quantum computing and quantum key distribution. However, the problem of quantifying the…
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system $(X, \mathcal{X}, \mu, T)$ is partially rigid if there is a constant $\delta…
Quantum coherence and non-Markovianity of an atom in dissipative cavity under weak measurement are investigated in this work. We find that, the quantum coherence obviously depends on the atomic initial state, the strength of the weak…
We describe the quantum phase transition of a Fermi gas occurring when the quasiparticle excitation energy has a minimum in momentum space which crosses zero on a sphere of radius k_0 \neq 0. The quasiparticles have a universal interaction…
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation $\phi$ acting on finite-dimensional quantum states. By reducing this problem to the problem…
By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the…
The structures of the enveloping semigroups of certain elementary finite- and infinite-dimensional distal dynamical systems are given, answering open problems posed by Namioka in 1982. The universal minimal system with (topological)…
We consider d-minimal expansions of ordered fields. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied…
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…
In this work, we investigate the dynamics of quantum correlations captured by entropic and geometric measures of discord under the influence of dissipative channels for widely used two qubit X state with maximally mixed marginals.…
A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. Evolution equations are shown to depend on higher-order gradients of the Hamiltonian, which are incorporated via their equations of…
The physics of quantum electromagnetism in an absorbing medium is that of a field of damped harmonic oscillators. Yet until recently the damped harmonic oscillator was not treated with the same kind of formalism used to describe quantum…
We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We…