Related papers: Wandering range of robust quantum symmetries
We revisit the notions of the quantum-mechanical sojourn time in the context of the quantum clocks to enquire whether the sojourn time be clocked without the clock affecting the dynamics of the wave motion. Upon recognizing that the…
The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…
Quantum state tomography is a core task in quantum system identification. Real experimental conditions often deviate from nominal designs, introducing errors in both the measurement devices and the Hamiltonian governing the system's…
Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $\mathcal{PT}$-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary…
We focus on recurrent random walks in random environment (RWRE) on Galton-Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers [AC18], [AdR17] and [dR16].…
The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is studied. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two…
We study random walks on the lampshuffler group $\mathrm{FSym}(H)\rtimes H$, where $H$ is a finitely generated group and $\mathrm{FSym}(H)$ is the group of finitary permutations of $H$. We show that for any step distribution $\mu$ with a…
The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…
In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional…
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
Using an approach to open quantum systems based on the effective non-Hermitian Hamiltonian, we fully describe transport properties for a paradigmatic model of a coherent quantum transmitter: a finite sequence of square potential barriers.…
Given a real-valued positive semidefinite matrix, Williamson proved that it can be diagonalised using symplectic matrices. The corresponding diagonal values are known as the symplectic spectrum. This paper is concerned with the stability of…
We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + \beta V(\omega t)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a…
The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
Consider a multichannel closed ring with disorder. In the semiclassical treatment its conductance is given by the Drude formula. Quantum mechanics challenge this result both in the limit of strong disorder (eigenstates are not…