1,720,974 research outputs found
Torus as phase space: Weyl quantization, dequantization, and Wigner formalism
No full textThe Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of theWigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols. Published by AIP Publishing
Stability of the gapless pure point spectrum of self-adjoint operators
No full textWe consider a self-adjoint operator T on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of T and on the bounded perturbation V ensuring the global stability of the spectral nature of T + epsilon V, epsilon is an element of R
The semiclassical limit of a quantum Zeno dynamics
Full text linkMotivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant h -> 0 and large quantum number N -> infinity, with hN kept fixed. In a suitable topology, the limit is the discontinuous symbol p chi(D) (x, p) where chi(D) is the characteristic function of the classically permitted region D in phase space. A refined analysis shows that the symbol is asymptotically close to the function p chi((N))(D) (x, p), where chi((N))(D) is a smooth version of chi(D) related to the integrated Airy function. We also discuss the limit from a dynamical point of view
Classical echoes of quantum boundary conditions
Full text linkWe consider a non-relativistic particle in a one-dimensional box with all possible quantum boundary conditions that make the kinetic-energy operator self-adjoint. We determine the Wigner functions of the corresponding eigenfunctions and analyze in detail their classical limit, governed by their behavior in the high-energy regime. We show that the quantum boundary conditions split into two classes: all local and regular boundary conditions collapse to the same classical boundary condition, while a dependence on singular non-local boundary conditions persists in the classical limit
On the inversion of the Radon transform: standard versus M2 approach
No full textWe compare the Radon transform in its standard and symplectic formulations and argue that the analytical
inversion of the latter is easier to perform
Quantum Zeno effect and dynamics
No full textIf frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula, we will give a characterization of the quantum Zeno effect for finite-rank projections in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its -- not necessarily bounded from below -- generator as a generalized mean value Hamiltonian
Large-time limit of the quantum Zeno effect
No full textIf very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝N α. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α ≥ 1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods
Tomography: mathematical aspects and applications
No full textIn this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford–Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations
Robustness of quantum symmetries against perturbations
No full textWe investigate quantum symmetries in terms of their large-time stability with respect to perturbations of the Hamiltonian. We find a complete algebraic characterization of the set of symmetries robust against a single perturbation and we use such result to characterize their stability with respect to arbitrary sets of perturbations
Nonlinear waves in adhesive strings
Full text linkWe study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state, beyond such a value the stress discontinuously drops to zero. Therefore the semilinear equation is characterized by a source term presenting jump discontinuity. Well-posedness of the initial boundary value problem of Neumann type, as well as qualitative properties of the solutions are studied and the evolution of different initial conditions are numerically investigated
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