Related papers: Semiclassical limits, Lagrangian states and coboun…
In spatial dimensions d >= 2, Kondo lattice models of conduction and local moment electrons can exhibit a fractionalized, non-magnetic state (FL*) with a Fermi surface of sharp electron-like quasiparticles, enclosing a volume quantized by…
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincar\'e transformation. The ground state, vacuum, is singlet and one particle states are transformed as…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
We give an exponentially-accurate normal form for a Lagrangian particle moving in a rotating shallow-water system in the semi-geostrophic limit, which describes the motion in the region of an exponentially-accurate slow manifold (a region…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
Let $\varphi$ be a univalent non-elliptic self-map of the unit disc $\mathbb D$ and let $(\psi_{t})$ be a continuous one-parameter semigroup of holomorphic functions in $\mathbb D$ such that $\psi_{1}\neq\mathrm{id}_{\mathbb D}$ commutes…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…
Transmission through potential barriers is a fundamental problem in quantum mechanics. While semiclassical methods can approximate certain aspects of transmission, they fail to capture the intrinsically quantum interference associated with…
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting…
We consider Lifshits' model of a quantum particle subject to a repulsive Poissonian random potential and address various issues related to the influence of a constant magnetic field on the leading low-energy tail of the integrated density…
For a time dependent family of probability measures $(\rho_t)_{t\ge 0}$ we consider a kinetic-type evolution equation $\partial \phi_t/\partial t + \phi_t = \widehat{Q} \phi_t$ where $\widehat{Q}$ is a smoothing transform and $\phi_t$ is…
We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. In particular, we obtain a generalisation of Ellis's joint continuity theorem. We also investigate the…
`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to…
We study the thermal properties of quantum field theories (QFT) with three-leg interaction vertices $g\varphi^{3}$ and $gS\varphi^{2}$ ($\varphi$ and $S$ being scalar fields), which constitute the relativistic counterpart of the Yukawa…
Two-parameter sets of solutions to the classical field equations in the massless $\phi^4$ model and SU(2) gauge theory are found, each solution presumably describing a multi-particle instanton-like transition at high energy. In the limit of…
In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent…
We present a set of quantum-mechanical Hamiltonians which can be written as the $F^{\,\rm th}$ power of a conserved charge: $H=Q^F$ with $[H,Q]=0$ and $F=2,3,...\, .$ This new construction, which we call {\it fractional}\/ supersymmetric…
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonically associated to the \textbf{standard semi--circle random…
In this paper, we consider the following singularly perturbed fractional Kirchhoff problem \begin{equation*} \Big(\varepsilon^{2s}a+\varepsilon^{4s-N}…