Spreading of atomic wave packets and semiclassical chaos

JETP Letters - The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated....     

Spreading of atomic wave packets and semiclassical chaos

The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast “spreading” of quantized wave packets in the momentum space is observed. Thus, deterministic chaos “imitates” the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.     

On classical and semiclassical properties of the Liouville theory with defects

Physics of Atomic Nuclei - The Lagrangian of the Liouville theory with topological defects is analyzed in detail and general solution of the corresponding defect equations of motion is found. We...     

Interaction of atomic wave packets with four-wave mixing: detection of rubidium and potassium wave packets by coherent ultraviolet emission

The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7相似文献   

Generation of soliton-like wave packets and wave packets with linear phase modulation in gaining optical wave-guides with saturable nonlinearity

We have considered the dynamics of soliton-like pulses and stable frequency-modulated self-similar pulses in an active medium with saturable nonlinearity and a parabolic refractive-index profile. We show that, based on gaining gradient fibers with a parabolic distribution of the refractive index and saturable nonlinearity, it is possible to create complexes that ensure generation of laser pulses with a high (above 1 TW) peak power.     

Impossibility of simultaneous localization of wave packets in energy and in configuration space

We consider Schrödinger Hamiltonians H, the scalar and vector potential of which may be singular on a closed set of measure zero. Sufficient conditions are given implying that no state vector can have compact support both in the spectral representation of H and in configuration space. These conditions are verified if the scalar potential is locally not too singular as well as for certain strongly singular potentials.     

Integrable quantum field theories and conformal field theories from lattice models in the light-cone approach

The light-cone lattice approach to two-dimensional quantum field theories is generalized to a large class of vertex models with any number of possible states per link and any simple Lie group of symmetry. Starting from a given lattice model, different scaling limits are defined leading to conformal field theories or to massive integrable quantum field theories, for which the lattice hamiltonian, momentum and currents are constructed. For a large set of models, the complete mass spectrum is also exhibited. Our approach applies equally well to chiral fermionic theories (like the chiral Gross-Neveu) and to bosonic models like the principal chiral model.     

Integrable models for the dynamics of a longitudinal-transverse acoustic wave in a crystal with paramagnetic impurities

We theoretically study the evolution of longitudinal-transverse acoustic pulses propagating parallel to an external magnetic field in a system of resonant paramagnetic impurities with an effective spin S=1/2. For equal group velocities of the longitudinal and transverse waves, the pulse dynamics is shown to be described by evolution equations. In limiting cases, these equations reduce to equations integrable in terms of the inverse scattering transform method (ISTM). For the most general integrable system of equations that describes the dynamics of acoustic pulses outside the scope of the slow-envelope approximation, we derive the corresponding ISTM equations. These equations are used to find a soliton solution and a self-similar solution. The latter describes the leading edge of the packet of acoustic pulses generated when the initial unstable state of a spin system decays. Analysis of our solutions and models indicates that the presence of a longitudinal acoustic wave leads not only to a change in the amplitude and phase of the transverse wave but also to a qualitatively new dynamics of sound in such a medium.     

FRW minisuperspace with local N=4 supersymmetry and self‐interacting scalar field

A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ?1. At order λ⁰ we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ¹, where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial ( = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time‐reparametrization) can be relevant concerning the issue of supersymmetry breaking.     

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.     

The correspondence between Casimir pressure and energy in one-dimensional field models

We propose a method of calculation of Casimir pressure using the Green function for one-dimensional case. This method yields the renormalized pressure if an external field is absent, otherwise it permits us to calculate the dependence of pressure at one boundary on the other boundary’s coordinate. The calculated pressure permits one to obtain the Casimir energy for the systems under consideration.     

Stationary wave packets in the Kerr nonlinear media with imaginary harmonic potential and linear gain

The existence of stationary wave packets in the nonlinear Kerr media with an imaginary harmonic potential and a linear gain is investigated. By employing a variational approach the existence of stable bright solitons is shown for the case of a defocusing nonlinearity. In focusing nonlinear media, the bright solitons have been shown to be unstable. The predictions of variational approach are confirmed by numerical simulations of the full modified NLS equation. The predicted stationary localized wave packets can be observed in a quasi-one-dimensional BEC with an imaginary optical potential and atoms feeding.     

The phase delay and its complex time: From stationary states up to wave packets

Complex time is often invoked about tunneling effect where the classical phase delay is completed with a crucial filter effect. Usually the complex times are obtained by considering the flux–flux correlation function, but this can be obtained by a very simple approach using the search of the maximum of the generalized complex phase function, including the amplitude of the wave function. Various aspects of the phase delay are presented in the case of wave packets impinging on simple or resonant quantum barriers.     

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

A new car-following model is proposed based on the full velocity difference model(FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau(TDGL) equation and the modified Korteweg-de Vries(mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.