Related papers: From the quantum Boltzmann operator to the quantum…
The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator…
We develop a Boltzmann-type quantum transport theory for interacting fermion and scalar fields including both flavour and particle-antiparticle mixing. Our formalism is based on the coherent quasiparticle approximation (cQPA) for the…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We consider various iterative algorithms for solving the linear equation $ax=b$ using a quantum computer operating on the principle of quantum annealing. Assuming that the computer's output is described by the Boltzmann distribution, it is…
This paper deals with the comparison between the strong Thomas-Fermi theory and the quantum mechanical ground state energy of a large atom confined to lowest Landau band wave functions. Using the tools of microlocal semiclassical spectral…
The confluence of quantum mechanics and complexity, which leads to the emergence of rich, exotic states of matter, motivates the extension of our concepts of quantum ordering. The twin concepts of spontaneously broken symmetry, described in…
Evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct a special generating functional for density operators of the quantum fields with different initial conditions.…
We study a possible scenario of the Lorentz symmetry violation background that allows us to build an analogue of the Landau system for a nonrelativistic Dirac neutral particle interacting with a field configuration of crossed electric and…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
We present a way of defining the Dirichlet-to-Neumann operator on general Hilbert spaces using a pair of operators for which each one's adjoint is formally the negative of the other. In particular, we define an abstract analogue of trace…
Given a positive operator-valued measure $\nu$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
In 1978 E. De Giorgi formulated a conjecture concerning the one-dimensional symmetry of bounded solutions to the elliptic equation \Delta u=F'(u), which are monotone in some direction. In this paper we prove the analogous statement for the…
We consider the Schr\"odinger operator in the plane with delta-potential supported by a curve. For the cases of an infinite curve and a finite loop we give estimates on the lower bound of the spectrum expressed explicitly through the…
The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic.…
In this article we explore ideas from quantum entanglement which can be meaningfully formulated and tested in the collider environment. We propose Bell-type inequalities as operator-level diagnostics of quantum incompatibility in…
Quantum Electrodynamics may be formulated as a Quantum Field Theory , and also as relativistic quantum mechanics by introduction of the Feynman-Stueckelberg parameter. As stated by M. Srednicki ({\it Quantum Field Theory}, Cambridge…
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the…
This paper presents a new perspective on unifying all fundamental interactions--gravitational, electromagnetic, weak and strong--based on stochastic processes rather than conventional quantum mechanics. Earlier work by Nelson, Kac and…