Quantum states transfer between coupled fields

We study the exchange of states in coupled fields along their time evolution. The coupling is described by a quadratic form in terms of annihilation and creation operator in the field Hamiltonian. An analytical approach is employed to describe the time evolution of the field state in Fock's space and the conditions for an arbitrary initial states to be transferred with 100% fidelity is determined. We show that only for initial states C₀|0>+C_N|N>, this situation can occurs. The important |1〉↔|0〉 qubits transfer is a particular case of this transference of number state. The relation between the coupling constant and characteristic field frequencies for complete state transference is also determined.     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

A realization of physical states in the Farri representation for the electroweak theory with a non-Abelian external field in the Rξ-gauge

A realization is found of the initial and final physical states in the Farri representation for the standard electroweak theory in the R-gauge with a free non-Abelian external field. It is shown that in the physical sector the spectrum of the Hamiltonian of the theory at the initial and final moments of time is positive definite and the evolution of the physical states does not lead them out of the physical subspace.Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 98–103, March, 1993.     

Dynamic and spectral mixing in nanosystems

In the framework of a simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities 1; 1 ± δ typical for vibrational states in many nanosize systems (e.g., large molecules containing CH₂ fragment chains, or carbon nanotubes). We show that quantum evolution of the system is determined by a dimensionless parameter δΓ, where Γ is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. When δΓ > 1 spectral chaos destroys recurrence cycles and the system state evolution is stochastic-like. In the opposite limit δΓ < 1 dynamics is regular up to the critical recurrence cycle k _c and for larger k > k _c dynamic mixing leads to quasi-stochastic time evolution. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems in the spectral window 10¹¹–10¹³ s⁻¹     

Low temperature asymptotic behaviours of the correlation functions in the one-dimensional fermi gas

The g-model of the one-dimensional (1-D) Fermi gas including the same site interaction g₄ is investigated in the self-consistent harmonic approximation (SCHA) for the Bosonized Hamiltonian. The asymptotic form of the gap of the spin-density excitation is determined at low temperatures. It is found that the phase transition is of first order and the transition exists if g₁₆ < 0 but does not if g₁₆ > 0. The correlation functions for the order parameters of the charge-density wave (CDW) and singlet-superconductor (SS) are evaluated at low temperatures.     

A Light-Cone QCD Inspired Meson Model with a Relativistic Confining Potential in Momentum Space

For describing the radial excited states a relativistic confining potential in momentum space is included in the meson effective light-cone Hamiltonian. The meson eigen equations are transformed from the front form to the instant form and formulated in total angular representation. Details about numerically solving these equations are discussed, mainly focusing on treating singularities arising from one-gluon exchange interactions and confinement. The results of pseudo-scalar mesons indicate that the improved meson effective light-cone Hamiltonian can describe the ground states and radial excited states well. Some radial excited states are also predicted and waiting for experimental test.     

Fermion Coherence Hamiltonians

We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence Hamiltonian, which is of the more general form of the nonstationary forced bosonic oscillator. If however one admits Grassmann variables as Hamiltonian parameters then the coherence Hamiltonian takes again the form of (Grassmannian fermionic) forced oscillator.     

Extraction of the spurious states from the solution of the motion equation within the random phase approximation

The general form of nuclear Hamiltonian equation of motion is derived within the Random Phase Approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the equations of motion is shown. The general method of extraction of spurious states from the solution of the RPA equations of motion is proposed.     

On the Lorentz group SO(3, 1), geometrical supersymmetric action for particles, and square root operators

In this work the problem of the square-root quantum operators is analyzed from the theoretical group point of view. To this end, we considered the relativistic geometrical action of a particle in the superspace in order to quantize it and to obtain the spectrum of physical states with the Hamiltonian remaining in the natural square-root form. The generators of group SO(3, 1) are introduced and the quantization of this model is performed completely. The obtained spectrum of physical states and the Fock construction for the physical states from the Hamiltonian operator in square-root form was proposed, explicitly constructed, and compared with the spectrum and Fock construction obtained from the Hamiltonian in the standard form (i.e., quadratic in momenta). We show that the only states that the square-root Hamiltonian can operate with correspond to the representations with the lowest weights λ = 1/4 and 3/4 with four possible (nontrivial) fractional representations for the group decomposition of the spin structure. The text was submitted by the author in English.     

Few-baryon systems in the SU(2) Skyrme model

Classically stable solitons with baryon number 1, 2, 3, and 4 have been investigated in the framework of a very general assumption about the form of the solutions for the Skyrme-model equations. Some of the solitons have a toroidal structure and some of them are more complicated. The effective quantum-mechanical Hamiltonian and its spectrum are obtained by using the collective-variable method. All the states with quantum numbers of light nuclei have binding energies greater than the experimental ones. Some of the calculated states containing antibaryons as substructure units could appear as compound nuclear states in experiments with stopped antibaryons.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

The transformation of the effective rotational Hamiltonian H of nonrigid X ₂ Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H₂O molecule.     

Antivortices due to competing orbital and paramagnetic pair-breaking effects

Thermodynamically stable vortex—antivortex structures in a quasi-twodimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle θ. The spectrum of possible states contains the ordinary vortex state (for large θ) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state (for θ = 0) as limits. The quasi-classical equations are solved nearH _c2 for arbitrary θ and it is shown that stable states with co-existing vortices and antivortices exist in a small interval close to θ= 0. The results are compared with recent predictions of antivortices in mesoscopic samples.     

Metastable States in Parametrically Excited Multimode Hamiltonian Systems

 Consider a linear autonomous Hamiltonian system with m time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, of bound states directly to bound states, as well as coupling among bound states, which is mediated by continuum modes. Our analysis elucidates these interactions and we prove the metastability (long life time) and eventual decay of bound states for a large class of systems. The key hypotheses for the analysis are: appropriate local energy decay estimates for the unperturbed evolution operator, restricted to the continuous spectral part of the Hamiltonian, and a matrix Fermi Golden rule condition, which ensures coupling of bound states to continuum modes. Problems of the type considered arise in many areas of application including ionization physics, quantum molecular theory and the propagation of light in optical fibers in the presence of defects. Received: 13 March 2002 / Accepted: 2 January 2003 Published online: 14 April 2003 Communicated by J.L. Lebowitz     

Ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic quantum gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive (U < 0) asymmetric (t_↑≠t_↓) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. We present the phase diagram of the homogeneous system and numerical results for unbalanced Fermi-mixtures obtained within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.     

A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces

In this paper, we give a KAM theorem for a class of infinite dimensional nearly integrable Hamiltonian systems. The theorem can be applied to some Hamiltonian partial differential equations in higher dimensional spaces with periodic boundary conditions to construct linearly stable quasi–periodic solutions and its local Birkhoff normal form. The applications to the higher dimensional beam equations and the higher dimensional Schrödinger equations with nonlocal smooth nonlinearity are also given in this paper.     

On Departures from the Lee, Oehme and Yang Approximation

The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in the assumptions and approximations used in the standard derivation of the LOY effective Hamiltonian, H_LOY, governing this time evolution are found. Eliminating these inconsistencies and using the LOY method, approximate formulae for the effective Hamiltonian, H_||, governing the time evolution in this subspace (improving those obtained by LOY) are derived. It is found, in contradistinction to the standard LOY result, that in the case of neutral kaons (K ₀ |H_|||K ₀ –¯K ₀ |H_|||¯K ₀ ), cannot take the zero value if the total system the preserves CPT-symmetry. Within the use of the method mentioned above formulae for H_|| acting in the three state (three dimensional) subspace of states are also found.     

Jet spaces in modern Hamiltonian biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. This is the time-dependent generalization of an ‘ordinary’ autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. In our view, this time-dependent energetic approach is much more realistic than the autonomous one. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system.