Search results for "Hamiltonian"
showing 10 items of 662 documents
Action-Angle Variables
2001
In the following we will assume that the Hamiltonian does not depend explicitly on time; ∂H/∂t = 0. Then we know that the characteristic function W(q i , P i ) is the generator of a canonical transformation to new constant momenta P i , (all Q i , are ignorable), and the new Hamiltonian depends only on the P i ,: H = K = K(P i ). Besides, the following canonical equations are valid: $$ \dot Q_i = \frac{{\partial K}} {{\partial P_i }} = v_i = const. $$ (1) $$ \dot P_i = \frac{{\partial K}} {{\partial Q_i }} = 0. $$ (2)
Types of Motion in the Oblate Planet Problem
1985
We consider a mass point in the gravitational field of an oblate planet and in a meridianal plane. The Hamiltonian of the problem is: $$ \frac{1}{2}\left( {p_r^2 + \frac{{p_{\theta }^2}}{{{r^2}}}} \right) - \frac{1}{r} - \frac{\varepsilon }{{{r^3}}}\left( {1 - 3{{\sin }^2}\theta } \right) $$ .
Pizza-cutter’s problem and Hamiltonian paths
2019
Summary. The pizza-cutter’s problem is to determine the maximum number of pieces that can be made with n straight cuts through a circular pizza, regardless of the size and shape of the pieces. For ...
An example of cancellation of infinities in the star-quantization of fields
1993
Within the *-quantization framework, it is shown how to remove some of the divergences occurring in theλo 2 4 -theory by introducing aλ-dependent *-product cohomologically equivalent to the normal *-product.
Appearances of pseudo-bosons from Black-Scholes equation
2016
It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schr\"odinger equation expressed in terms of a non self-adjoint hamiltonian. We show how {\em pseudo-bosons}, linear or not, naturally arise in this context, and how they can be used in the computation of the pricing kernel.
Quasi-continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature
2013
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard mo…
Singlet and triplet excitons in conjugated polymers.
1992
Exciton states in conjugated polymers are theoretically studied in the Su-Schrieffer-Heeger model supplemented by long-range Coulomb interactions. The relationship between exciton energies and basic interaction parameters is clarified, demonstrating the special nature of one-dimensional excitons. The binding energies of the lowest singlet and triplet excitons depend sensitively upon the on-site Coulomb energy. Relevant experiments in polydiacetylene can be explained by the present model using moderate interaction strength.
Squeezing in a two-photon Dicke hamiltonian
1986
Abstract The single-mode, two-level atom Dicke hamiltonian with two-photon atom-field coupling is treated exactly and it is shown to yield a certain degree of squeezing in the field variables. This result is briefly discussed in connection with the previously shown absence of squeezing in the two-photon laser model.
Quantum many-body dynamics of coupled double-well superlattices
2008
We propose a method for controllable generation of non-local entangled pairs using spinor atoms loaded in an optical superlattice. Our scheme iteratively increases the distance between entangled atoms by controlling the coupling between the double wells. When implemented in a finite linear chain of 2N atoms, it creates a triplet valence bond state with large persistency of entanglement (of the order of N). We also study the non-equilibrium dynamics of the one-dimensional ferromagnetic Heisenberg Hamiltonian and show that the time evolution of a state of decoupled triplets on each double well leads to the formation of a highly entangled state where short-distance antiferromagnetic correlatio…
Quantum Dynamics of Strongly Interacting Boson Systems: Atomic Beam Splitters and Coupled Bose-Einstein Condensates
2001
An effective boson Hamiltonian applicable to atomic beam splitters, coupled Bose-Einstein condensates, and optical lattices can be made exactly solvable by including all $n$-body interactions. The model can include an arbitrary number of boson components. In the strong interaction limit the model becomes a quantum phase model, which also describes a tight-binding lattice particle. Through exact results for dynamic correlation functions, it is shown how the previous weak interaction dynamics of these systems are extended to strong interactions, now becoming relevant in the experiments. The effect of the number of boson components is also analyzed.