Search results for "Ham"
showing 10 items of 2612 documents
Beyond the Runge–Gross Theorem
2012
The Runge–Gross theorem (Runge and Gross, Phys Rev Lett, 52:997–1000, 1984) states that for a given initial state the time-dependent density is a unique functional of the external potential. Let us elaborate a bit further on this point. Suppose we could solve the time-dependent Schrodinger equation for a given many-body system, i.e. we specify an initial state \(| \Uppsi_0 \rangle\) at \(t=t_0\) and evolve the wavefunction in time using the Hamiltonian \({\hat{H}} (t).\) Then, from the wave function, we can calculate the time-dependent density \(n (\user2{r},t).\) We can then ask the question whether exactly the same density \(n(\user2{r},t)\) can be reproduced by an external potential \(v^…
Time-Independent Canonical Perturbation Theory
2001
First we consider the perturbation calculation only to first order, limiting ourselves to only one degree of freedom. Furthermore, the system is to be conservative, ∂ H∕∂ t = 0, and periodic in both the unperturbed and perturbed case. In addition to periodicity, we shall require the Hamilton–Jacobi equation to be separable for the unperturbed situation. The unperturbed problem H0(J0) which is described by the action-angle variables J0 and w0 will be assumed to be solved. Thus we have, for the unperturbed frequency: $$\displaystyle{ \nu _{0} = \frac{\partial H_{0}} {\partial J_{0}} }$$ (10.1) and $$\displaystyle{ w_{0} =\nu _{0}t +\beta _{0}\;. }$$ (10.2) Then the new Hamiltonian reads, up t…
Models for highway traffic and their connections to thermodynamics
2007
Models for highway traffic are studied by numerical simulations. Of special interest is the spontaneous formation of traffic jams. In a thermodynamic system the traffic jam would correspond to the dense phase (liquid) and the free flowing traffic would correspond to the gas phase. Both phases depending on the density of cars can be present at the same time. A model for a single lane circular road has been studied. The model is called the optimal velocity model (OVM) and was developed by Bando, Sugiyama, et al. We propose here a reformulation of the OVM into a description in terms of potential energy functions forming a kind of Hamiltonian for the system. This will however not be a globally …
Poincaré Surface of Sections, Mappings
2001
We consider a system with two degrees of freedom, which we describe in four-dimensional phase space. In this (finite) space we define an (oriented) two-dimensional surface. If we then consider the trajectory in phase space, we are interested primarily in its piercing points through this surface. This piercing can occur repeatedly in the same direction. If the motion of the trajectory is determined by the Hamiltonian equations, then the n + 1-th piercing point depends only on the nth. The Hamiltonian thus induces a mapping n → n + 1 in the “Poincare surface of section” (PSS). The mapping transforms points of the PSS into other (or the same) points of the PSS. In the following we shall limit …
Kinetic exchange Hamiltonian for orbitally degenerate ions
1998
Abstract A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The highly anisotropic effective Hamiltonian is expressed in terms of unit irreducible tensor operators and spin operators. All parameters of the exchange Hamiltonian are expressed through relevant transfer integrals, crystal field and Racah parameters for the metal ions. As an example the edge-shared ( D 2 h ) bioctahedral cluster is discussed and some comments on the considerations of Anderson, Goodenough and Kanamori and McConnell are given.
Magnetic Exchange between Orbitally Degenerate Ions: A New Development for the Effective Hamiltonian
1998
A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The constituent multielectron metal ions are assumed to be octahedrally coordinated, and strong crystal field scheme is employed, making it possible to take full advantage from the symmetry properties of the fermionic operators and collective electronic states. In the framework of the microscopic approach, the highly anisotropic effective Hamiltonian of the kinetic exchange is constructed in terms of spin operators and standard orbital operators (matrices of the unit cubic irreducible tensors). As distinguished from previous considerations, the effective Hamiltonian is derived for a most genera…
Tunneling-charging Hamiltonian of a Cooper-pair pump
2001
General properties of the tunneling-charging Hamiltonian of a Cooper pair pump are examined with emphasis on the symmetries of the model. An efficient block-diagonalization scheme and a compatible Fourier expansion of the eigenstates is constructed and applied in order to gather information on important observables. Systematics of the adiabatic pumping with respect to all of the model parameters are obtained and the link to the geometrical Berry's phase is identified.
Entanglement dynamics in a spin star system
2009
The implementation of more and more efficient nanodevices exploitable in applicative contexts like for example quantum computers often requires a highly challenging miniaturizing process aimed at packing a huge number of point-like basic elements whose dynamics mimics indeed that of a qubit. Stimulated by such a requirement, over the last few years theoretical schemes using the language of the spin ½ system models have been investigated. The main reason is that besides the simple dynamical behaviour of each elementary constituent these Hamiltonian models do indeed capture basic ingredients of several physical situations differing one another mainly for the numerical values of some relevant …
The bound state in the spectrum of the Lee–Friedrichs Hamiltonian
2000
Abstract The spectrum of the Lee–Friedrichs Hamiltonian, describing a two-level system embedded in a continuum, is considered. An appropriate discretization of the field modes is performed before taking the continuum limit. It is shown that the existence of an eigenstate with negative energy (bound state) is related to the nonanalyticity of the Friedrichs spectral representation. This negative energy state is a dressed state and its physical properties are studied in some significant cases.
Exchange Interactions II: Spin Hamiltonians
1996
In Part I the physical mechanism of exchange interactions have been discussed. In this part we introduce the general concept of spin-hamiltonian. Isotropic exchange hamiltonian for many-electron polynuclear clusters (Heisenberg-Dirac-van Vleck-HDVV model [1-6]) will be derived. Spin-hamiltonian approach allows to separate the full exchange problem into two independent ones: 1) evaluation of the energy levels of the exchange system considering Jij as a set of semiempirical parameters, and 2) quantum mechanical calculation of exchange parameters with the aim of elucidation of the main physical mechanisms of the exchange coupling. In this part we shall focus on the problem of calculation of sp…