Search results for "Hamiltonian"
showing 10 items of 662 documents
Inverse eigenvalue problem for normal J-hamiltonian matrices
2015
[EN] A complex square matrix A is called J-hamiltonian if AT is hermitian where J is a normal real matrix such that J(2) = -I-n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem. (C) 2015 Elsevier Ltd. All rights reserved.
Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian.
2011
We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The "picture-change" effect in the calculation of p…
Correlation at low temperature I. Exponential decay
2003
Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general Hamiltonian function with pair interaction. The novelty, as compared to [2,20], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in [2,20]. We prove that this Laplacian has a spectral gap above zero…
The Poincar\'e-Cartan Form in Superfield Theory
2018
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.
The Principles of Canonical Mechanics
2010
Canonical mechanics is a central part of general mechanics, where one goes beyond the somewhat narrow framework of Newtonian mechanics with position coordinates in the three-dimensional space, towards a more general formulation of mechanical systems belonging to a much larger class. This is the first step of abstraction, leaving behind ballistics, satellite orbits, inclined planes, and pendulum-clocks; it leads to a new kind of description that turns out to be useful in areas of physics far beyond mechanics. Through d’Alembert’s principle we discover the concept of the Lagrangian function and the framework of Lagrangian mechanics that is built onto it. Lagrangian functions are particularly …
Correlation at Low Temperature: II. Asymptotics
2004
The present paper is a continuation of ref. 4, where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends ref. 3 in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.
Spin texture motion in antiferromagnetic and ferromagnetic nanowires
2017
We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton equations of motion via Poisson brackets based on the Landau-Lifshitz-Gilbert phenomenology, and add dissipative dynamics via the evolution of the energy. We use this approach to study current induced domain wall motion and compute the drift velocity. For the antiferromagnetic case, we show that a nonzero magnetic moment is induced in the domain wall, which indicates that an additional application of a magnetic field would influence the antiferromagnetic do…
A consistent microscopic theory of collective motion in the framework of an ATDHF approach
1978
Based on merely two assumptions, namely the existence of a collective Hamiltonian and that the collective motion evolves along Slater determinants, we first derive a set of adiabatic time-dependent Hartree-Fock equations (ATDHF) which determine the collective path, the mass and the potential, second give a unique procedure for quantizing the resulting classical collective Hamiltonian, and third explain how to use the collective wavefunctions, which are eigenstates of the quantized Hamiltonian.
Non-Gaussian correlations imprinted by local dephasing in fermionic wires
2020
We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the non-equilibrium steady-state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime r…
Bi-homogeneity and integrability of rational potentials
2020
Abstract In this paper we consider natural Hamiltonian systems with two degrees of freedom for which Hamiltonian function has the form H = 1 2 ( p 1 2 + p 2 2 ) + V ( q 1 , q 2 ) and potential V ( q 1 , q 2 ) is a rational function. Necessary conditions for the integrability of such systems are deduced from integrability of dominate term of the potential which usually is appropriately chosen homogeneous term of V. We show that introducing weights compatible with the canonical structure one can find new dominant terms which can give new necessary conditions for integrability. To deduce them we investigate integrability of a family of bi-homogeneous potentials which depend on two integer para…