相关论文: Level Crossings in a PT-symmetric Double Well

We make a nodal analysis of the processes of level crossings in a model of quantum mechanics with a PT-symmetric double well. We prove the existence of infinite crossings with their selection rules. At the crossing, before the PT-symmetry…

Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods,…

Recently, level crossings in the energy bands of crystals have been identified as a key signature for topological phase transitions. Using realistic models we show that the parameter space controlling the occurrence of level coincidences in…

We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is…

We study the existence and location of the resonances of a $2\times 2$ semiclassical system of coupled Schr\"odinger operators, in the case where the two electronic levels cross at some point, and one of them is bonding, while the other one…

The sub-barrier pairs of energy levels of a Hermitian one-dimensional symmetric double well potential are known to merge into one, if the inter-well distance ($a$) is increased slowly. The energy at which the doublets merge are the ground…

A three level atom in $\Lambda$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a…

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits…

Due to the absence of degeneracy in one dimension, when a parameter, $\lambda$, of a potential is varied slowly the discrete energy eigenvalue curves, $E_n(\lambda)$, cannot cross but they are allowed to come quite close and diverge from…

The quasi-energy spectrum recently measured in experiments with a squeeze-driven superconducting Kerr oscillator showed good agreement with the energy spectrum of its corresponding static effective Hamiltonian. The experiments also…

The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…

Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…

We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with…

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger…

Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never…

Additive white noise may significantly increase the response of bistable systems to a periodic driving signal. We consider two classes of double-well potentials, symmetric and asymmetric, modulated periodically in time with period $1/\eps$,…

At high level density, two states avoid usually crossing at the critical value $a_{\rm cr}$ of the parameter $a$ by which the system is controlled. The wavefunctions of the two states are mixed in a finite parameter range around $a_{\rm…

Coupled pair of PT-symmetric square wells is studied as a prototype of a quantum system characterized by two manifestly non-Hermitian commuting observables. We demonstrate that there exists a domain of couplings where both the respective…

Unavoided crossings of the energy levels due to a variation of a real parameter are studied. It is found that after the quantum system in question passes through one of its energy-crossing points {\it alias} Kato's exceptional points (EP),…

Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…