Quantum signatures of chaos or quantum chaos?

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.     

Effects of an anisotropic parabolic potential and Coulomb’s impurity potential on the energy characteristics of asymmetrical semi-exponential CsI quantum wells

Because of its unique optoelectronic properties,people have studied the characteristics of polarons in various quantum well(QW)models.Among them,the asymmetrical semiexponential QW(ASEQW)is a new model for studying the structure of QWs in recent years.It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential(APCP)on the crystal’s properties,because some of the impurities,usually regarded as Coulomb’s impurity potential(CIP),will exist in the crystal more or less,and the APCP has flexible adjustment parameters.However,the energy characteristics of the ASEQW under the combined actions of impurities and APCP have not been studied,which is the motivation of this paper.Using the linear combination operation and Lee-Low-Pines unitary transformation methods,we investigate the vibrational frequency and the ground state energy of the strong coupling polaron in an ASEQW with the influences of the CIP at the origin of coordinates and APCP,and make a comparison between our results and previous literature’s.Our numerical results about the energy properties in the ASEQW influenced by the CIP and APCP may have important significances for experimental design and device preparation.     

Effect of isotope on state-to-state dynamics for reactive collision reactions ■ and ■ in ground state 1~2 A’’ and first excited 1~2 A’ potential energy surfaces

We carry out quantum scattering dynamics and quasi-classical trajectory(QCT) calculations for the O+H_2~+ reactive collision in the ground(1~2 A").nd first excited(1~2 A') potential energy surface.We calculate the reaction probabilities of O+H_2~+(v=0,j=0)→OH~++H and O+H_2~+(v=0,j=0)→OH+H~+reaction for total angular momentum J=0.The results calculated by QCT are consistent with those from quantum mechanical wave packet.Using the QCT method,we generate in the center-of-mass frame the product state-resolved integral cross-sections(ICSs);two commonly used generalized polarization-dependent differential cross-sections(PDDCS s),(2π/σ)(dσ_(00)/dω_t),(2π/σ)(dσ_(20)/dω_t));and three angular distributions of the product rotational vectors,p(θ_r),P(φ_r),and p(θ_r,φ_r).We discuss the influence on the scalar and vector properties of the potential energy surface,the collision energy,and the isotope mass.Since there are deep potential wells in these two potential energy surfaces,their kinetic characteristics are similar to each other and the isotopic effect is not obvious.However,the well depths and configurations of the two potential energy surfaces are different,so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.     

Simulation of quantum wells with ‘spikes’ and ‘dips’

The use of thin high-bandgap ‘spikes’ or thin low-bandgap ‘dips’ inside conventional rectangular quantum wells (QWs) gives supplementary flexibility in engineering intra- and inter-band energy level separation. The paper presents simulation and experimental studies on the effects of ‘spikes’ and ‘dips’ on the fundamental quantum well properties.     

Out-of-roundness and thermal energy effects on ‘ideally soft ferromagnets’

Infinite initial susceptibility is predicted in certain micro-magnetic computations of sufficiently small spheres and circular discs made of isotropic magnetic material. In this letter, it is argued that this result pertains only to perfectly round samples in the absence of thermal energy. It is expected, therefore, that much lower values of the initial susceptibility will be found on experimentally realizable samples at room temperature.     

Reactions in viscous media: potential and free energy surfaces in solvent–solute coordinates

We propose a universal definition of reaction-specific solvent coordinate, described in terms of molecular-dynamic trajectories of the solvent and suitable for a variety of reactions in viscous solvents. We then use molecular dynamics simulations to obtain two-dimensional potential energy and free energy surfaces of model liquid phase isomerisation reactions in solvent–solute coordinates and discuss factors determining their topography.     

Dynamics of Bose–Einstein condensate in a harmonic potential and a Gaussian energy barrier

We have studied the dynamics of Bose–Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.     

Dynamics of a cold quantum gas in a δ-split one-dimensional potential well

Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.     

Effect of exchange–correlation on quantum ion-acoustic soliton energy

The electrons exchange–correlation influence on the energy carried by the quantum ion-acoustic soliton (QIAS) is succinctly discussed. Starting from the one-dimensional quantum hydrodynamic model (in which the term of exchange–correlation for electrons is included), a deformed Korteweg–de Vries-like equation is derived. It is found that the QIAS energy experiences a depletion as a result of quantum diffraction. This quantum energy depletion may be counteracted by the exchange–correlation effect. The present work can be viewed as a first step towards the investigation of the exchange–correlation effects on the dynamics of solitary waves in quantum plasmas.     

‘Measurement of quantum mechanical operators’ revisited

The Wigner-Araki-Yanase (WAY) theorem states a remarkable limitation to quantum mechanical measurements in the presence of additive conserved quantities. Discovered by Wigner in 1952, this limitation is known to induce constraints on the control of individual quantum systems in the context of information processing. It is therefore important to understand the precise conditions and scope of the WAY theorem. Here we elucidate its crucial assumptions, briefly review some generalizations, and show how a particular extension can be obtained by a simple modification of the original proofs. We also describe the evolution of the WAY theorem from a strict no-go verdict for certain, highly idealized, precise measurements into a quantitative constraint on the accuracy and approximate repeatability of imprecise measurements.     

Ehrenfest ‘phase-space’ trajectories and quantum chaos in He atom under strong,oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory (TDQFDFT)

Using a dynamical signature proposed earlier from our laboratory, quantum chaos in He atom interacting with strong, oscillating magnetic fields has been studied through a comparison between the nonlinear divergence of two neighbouring Ehrenfest ‘phase-space’ (EPS) trajectories differing slightly in initial conditions and the Loschmidt echo. The dynamical EPS signature can detect quantum chaos independently of the Loschmidt echo and in agreement with the latter, even for low-lying states, in the same spirit as that of classical chaos. This time-dependent signature extends the concept of quantum chaos to systems which have no classical counterparts and brings the concept of quantum chaos closer to that of classical chaos.     

Dynamics of wetting and Kramers’ theory

We investigate the potential link between Kramer’s treatment of rate processes and the molecular-kinetic theory of wetting. The results of recent large-scale simulations of dynamic wetting are used to illustrate and validate our analysis. We find that both theories predict that, for a given driving force, the velocity of the contact line is inversely proportional to the viscosity. They also predict that the velocity will depend with a negative exponent on the strength of solid-liquid interactions, which for simple systems can be represented to good approximation by the reversible work of adhesion Wa ⁰.     

Theoretical studies of three-dimensional potential energy surfaces using neural networks and rotational spectra of the Ar–N2 complex

ABSTRACT

A new three-dimensional potential energy surface (PES) of the Ar–N₂ van der Waals complex is constructed using the neural network method based on ab initio data points at the CCSD(T) level. The aug-cc-pVQZ basis set is employed for all atoms with midbond functions. The vibrationally averaged PES V₀₀ is characterised by a global T-shaped minimum which occurs at R = 3.715 Å, θ = 90.0° with a well depth of 98.779 cm^?1. Based on our three-dimensional PES, bound-state calculations are performed for three isotopomers of Ar–¹⁴N₂, Ar–¹⁵N₂, and Ar–¹⁴N¹⁵N, and several intermolecular vibrational states are assigned by analysing the wavefunctions. Moreover, the averaged structural parameters are calculated and the pure rotational transition frequencies with J = 0--6 are predicted. The spectroscopic constants are determined by fitting the rotational energy levels. The theoretical results are in good agreement with experimental data and this work gives more accurate results than those determined previously for the Ar–N₂ complex.     

Dynamics of 2×2 matrix non-Hermitian quantum systems on Bloch sphere

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely,the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point(EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.     

Supersymmetric quantum cosmology: a ‘Socratic’ guide

We calculate the classical limit effective action of the EPRL/FK spinfoam model of quantum gravity coupled to matter fields. By employing the standard QFT background field method adapted to the spinfoam setting, we find that the model has many different classical effective actions. Most notably, these include the ordinary Einstein–Hilbert action coupled to matter, but also an action which describes antigravity. All those multiple classical limits appear as a consequence of the fact that the EPRL/FK vertex amplitude has cosine-like large spin asymptotics. We discuss some possible ways to eliminate the unwanted classical limits.