Small polaron dynamics: A self-consistent nonlinear spin-field model

The motion of an electron strongly and locally coupled to the lattice deformation is considered as a dynamical system. Our study is based on a model where the electron remains to two adjacent diatomic molecules vibrating around positions which evolve in time as the charge distribution of the electron gradually shifts from one of the molecules to the other one. This model is cast into an intuitively more accesible model of spin $\text{1}\text{2}$ in an external field plus a reaction field. Within a semiclassical approach this is a Hamiltonian system expressed with two sets of action-angle variables. We show how the regular trajectories (describing the cooperative mechanism between the charge transfer and rearrangement of the molecular positions) in this phase space gradually disappear and global stochasticity sets in as either the ratio of the electron hopping rate over the electron-lattice coupling constant or the total energy is varied.     

Analytical results on the magnetization of the Hamiltonian Mean-Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.     

Complexifications and real forms of Hamiltonian structures

We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms. Received 18 October 2001 / Received in final form 24 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Improving Shortcuts to Non‐Hermitian Adiabaticity for Fast Population Transfer in Open Quantum Systems

It is still a challenge to experimentally realize shortcuts to adiabaticity (STA) for a non‐Hermitian quantum system since a non‐Hermitian quantum system's counterdiabatic driving Hamiltonian contains some unrealizable auxiliary control fields. In this paper, we relax the strict condition in constructing STA and propose a method to redesign a realizable supplementary Hamiltonian to construct non‐Hermitian STA. The redesigned supplementary Hamiltonian can be eithersymmetric or asymmetric. For the sake of clearness, we apply this method to an Allen‐Eberly model as an example to verify the validity of the optimized non‐Hermitian STA. The numerical simulation demonstrates that a ultrafast population inversion could be realized in a two‐level non‐Hermitian system.     

Reversible maps in two-degrees of freedom Hamiltonian systems

It has been shown that a sub-class of two-degrees of freedom Hamiltonian systems possesses a reversing symmetry discovered by Birkhoff in the restricted problem of three bodies. This mixed space-time reversing symmetry, which is different from the classical time reversal symmetry, can be shared by time-reversible as well as time-irreversible systems. Examples of time-irreversible systems which possess this reversing symmetry are the restricted problem of three bodies as shown by Birkhoff in 1915, and a special case of the motion of a rigid body with a fixed point discussed in this paper. If a Hamiltonian system possesses this Birkhoff reversing symmetry, then there exists a surface of section for which the corresponding Poincare map is Birkhoff-reversible. The Birkhoff-reversibility of this map may be used to study its global dynamics such as the locations and the distribution of the stable and unstable periodic points, the distribution of stable and chaotic regions, and the identification of the scattering regions. (c) 2002 American Institute of Physics.     

Plaquette expansion proof and interpretation

The plaquette expansion, a general non-perturbative method for calculating the properties of lattice Hamiltonian systems, is established up to the first two orders for an arbitrary system. This method employs an expansion of the Lanczos coefficients, the tridiagonal Hamiltonian matrix elements or equivalently the continued fraction coefficients of the resolvent, in a descending series in the size of the system. The coefficients of this series are formed from the low order cumulants or connected Hamiltonian moments. The lowest order approximation in the plaquette expansion corresponds to a gaussian model which is a consequence of the central limit theorem. The first nontrivial order yields a model with a spectrum on a bounded energy interval, becoming asymptotically uniform in the thermodynamic limit.     

统计物理的微观动力学基础

统计的基本出发点是研究系统具有的随机性,不同系统在不同情形下的宏观热力学性质起源于系统内部随机性的差异,通过对宏观热力学系统的微观非线性动力学进行研究探索，我们可以进一步更为深入地理解物态方程、相变等诸多的宏观热力学现象。本文通过哈密顿系统的非线性动力学研究，以及遍历性理论的动力学随机性研究对此问题进行了分析，研究表明，动力学系统的全局性混沌是系统统计成立的根本要素，系统的无限大自由度（热力学极限）已不是决定性的因素，人们可以在此基础上建立少自由度系统的统计力学及热力学。     

梯度磁场中静电波引起的粒子随机运动

本文讨论了一般非均匀梯度磁场下任意方向传播的静电波引起粒子随机运动的非线性效应。用正则久期扰动理论给出包含粒子周期运动和波振荡之间非线性共振的哈密顿量。根据Chirikov岛重叠条件给出一般梯度磁场下粒子进入随机态的临界波幅值。分析表明,相对均匀磁场,在弱非均匀情形下,该临界值降低,意味着粒子更易进入随机态。 关键词：     

Quantum chemical construction of a reduced reaction Hamiltonian and T 1 -relaxation and pure T 2 -dephasing rates for the proton transfer in 3-chlorotropolone

Separating multidimensional problems into that of a relevant system which is coupled to a bath of harmonic oscillators is a common concept in condensed phase theory. Focusing on the specific problem of intramolecular proton transfer in an isolated tropolone derivative, we consider the reactive proton moving in the plane of the molecule as the system and the remaining substrate normal modes as the bath. An all-Cartesian system-plus-substrate Hamiltonian is constructed employing density functional theory. It is then used to determine the temperature-dependent effective reduced reaction Hamiltonian and the state-to-state dissipation rates induced via the system-substrate coupling up to the bi-quadratic order. The important substrate modes for the T₁-relaxation and the pure T₂-dephasing rates, which are either intra- or inter-well in nature, are identified numerically and analyzed physically with molecular details. Received 19 November 2001 and Received in final form 19 February 2002     

Application of Greene's method and the MacKay residue criterion to the double pendulum

The double pendulum is a non-integrable Hamiltonian system which exhibits the scenario of transition to global chaos via the decay of a golden mean KAM torus. We apply Greene's method and the MacKay residue criterion and compute the threshold to global chaos. We find that MacKay's method is superior to Greene's since it requires much less numerical work but nevertheless gives accurate results.     

Inverse problem of the variational calculus for higher KdV equations

It is shown that the usual Hamilton's variational principle supplemented by the methodology of the integer-programming problem can be used to construct expressions for the Lagrangian densities of higher KdV fields. This is demonstrated with special emphasis on the second and third members of the hierarchy. However, the method is general enough for applications to equations of any order. The expressions for Lagrangian densities are used to calculate results for Hamiltonian densities that characterize Zakharov-Faddeev-Gardner equation. Received 27 January 2002 / Received in final form 6 May 2002 Published online 24 September 2002     

Controlling chaos by a modified straight-line stabilization method

By adjusting external control signal, rather than some available parameters of the system, we modify the straight-line stabilization method for stabilizing an unstable periodic orbit in a neighborhood of an unstable fixed point formulated by Ling Yang et al., and derive a more simple analytical expression of the external control signal adjustment. Our technique solves the problem that the unstable fixed point is independent of the system parameters, for which the original straight-line stabilization method is not suitable. The method is valid for controlling dissipative chaos, Hamiltonian chaos and hyperchaos, and may be most useful for the systems in which it may be difficult to find an accessible system parameter in some cases. The method is robust under the presence of weak external noise. Received 10 January 2001     

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators.The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian.Calculations are based on Lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities.     

Renormalization by continuous unitary transformations: one-dimensional spinless fermions

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the Hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension favorable results are obtained which agree well with the exact findings based on Bethe ansatz. Received 21 August 2002 / Received in final form 29 October 2002 Published online 31 December 2002     

On adiabatic N-soliton interactions and trace identities

We compare the Hamiltonian properties of the N-soliton solutions of the NLSE in the adiabatic approximation and show how it matches the Hamiltonian formulation for the complex Toda chain which describes the adiabatic N-soliton interactions. Received 21 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Pacemaker-guided noise-induced spatial periodicity in excitable media

We study the impact of subthreshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media. For this purpose, we examine two systems that both consist of diffusively coupled units. In the first case, the local dynamics of the units is driven by a simple one-dimensional model of excitability with a piece-wise linear potential. In the second case, a more realistic biological system is studied, and the local dynamics is driven by a model for calcium oscillations. Internal noise is introduced via the τ-leap stochastic integration procedure and its intensity is determined by the finite size of each constitutive system unit. We show that there exists an intermediate level of internal stochasticity for which the localized pacemaker activity maps best into coherent periodic waves, whose spatial frequency is uniquely determined by the local subthreshold forcing. Via an analytical treatment of the simple minimal model for the excitable spatially extended system, we explicitly link the pacemaker activity with the spatial dynamics and determine necessary conditions that warrant the observation of the phenomenon in excitable media. Our results could prove useful for the understanding of interplay between local and global agonists affecting the functioning of tissue and organs.     

Quantum computational gates with radiation free couplings

We examine a generic three level mechanism of quantum computation in which all fundamental single and double qubit quantum logic gates are operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. Under the time evolution imposed by these bias couplings the quantum state cycles between the two degenerate levels in the ground state and the quantum gates are realized by changing Hamiltonian at certain time intervals when the system collapses to a two state subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops in crossed electric and magnetic fields, with the output of the loop read out by using a quantum Hall effect aided mechanism. Received 26 March 2002 / Received in final form 8 July 2002 Published online 19 November 2002     

Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots

In this article we study the impact of the spin-orbit interaction on the electron quantum confinement for narrow gap semiconductor quantum dots. The model formulation includes: (1) the effective one-band Hamiltonian approximation; (2) the position- and energy-dependent quasi-particle effective mass approximation; (3) the finite hard wall confinement potential; and (4) the spin-dependent Ben Daniel-Duke boundary conditions. The Hartree-Fock approximation is also utilized for evaluating the characteristics of a two-electron quantum dot system. In our calculation, we describe the spin-orbit interaction which comes from both the spin-dependent boundary conditions and the Rashba term (for two-electron quantum dot system). It can significantly modify the electron energy spectrum for InAs semiconductor quantum dots built in the GaAs matrix. The energy state spin-splitting is strongly dependent on the dot size and reaches an experimentally measurable magnitude for relatively small dots. In addition, we have found the Coulomb interaction and the spin-splitting are suppressed in quantum dots with small height. Received 15 May 2001 / Received in final form 14 May 2002 Published online 13 August 2002