共查询到20条相似文献,搜索用时 31 毫秒
1.
Michał Dobrski 《Central European Journal of Physics》2007,5(3):313-323
In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by
canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time
independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian
for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.
相似文献
2.
R. Koç O. Özer H. Tütüncüler R. G. Yıldırım 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(3):375-383
We consider solutions of the 2×2 matrix Hamiltonian of
physical systems within the context of the asymptotic iteration
method. Our technique is based on transformation of the associated
Hamiltonian in the form of the first order coupled differential
equations. We construct a general matrix Hamiltonian which
includes a wide class of physical models. The systematic study
presented here reproduces a number of earlier results in a natural
way as well as leading to new findings. Possible generalizations
of the method are also suggested. 相似文献
3.
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. 相似文献
4.
Leonardo Castellani 《Annals of Physics》1982,143(2):357-371
We derive an algorithm for the construction of all the gauge generators of a constrained hamiltonian theory. Dirac's conjecture that all secondary first-class constraints generate symmetries is revisited and replaced by a theorem. The algorithm is applied to Yang-Mills theories and metric gravity, and we find generators which operate on the complete set of canonical variables, thus producing the correct transformation laws also for the unphysical coordinates. Finally we discuss the general structure of the Hamiltonian for constrained theories. We show how in most cases one can read off the first-class constraints directly from the Hamiltonian. 相似文献
5.
Sema Bilge Ocak Özlem Yeşiltaş Bengü Demircioğlu 《International Journal of Theoretical Physics》2008,47(7):1865-1876
We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism.
The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept
of squeezed boson systems has been applied two-mode bosonic Hamiltonian which is a squeezed one and is determined through
a differential equation. This differential equation is solved and energy eigenvalues are found approximately. 相似文献
6.
We show how to map a given n-qubit target Hamiltonian with bounded-strength k-body interactions onto a simulator Hamiltonian with two-body interactions, such that the ground-state energy of the target and the simulator Hamiltonians are the same up to an extensive error O(epsilon n) for arbitrary small epsilon. The strength of the interactions in the simulator Hamiltonian depends on epsilon and k but does not depend on n. We accomplish this reduction using a new way of deriving an effective low-energy Hamiltonian which relies on the Schrieffer-Wolff transformation of many-body physics. 相似文献
7.
8.
《Journal of Nonlinear Mathematical Physics》2013,20(1-2):12-27
Abstract We report on a new formulation of classical relativistic Hamiltonian mechanics which is based on a proper-time implementation of special relativity using a transformation from observer proper-time, which is not invariant, to system proper-time which is a canonical contact transformation on extended phase-space. This approach does not require the use of time as a fourth coordinate and so we prove that it satisfies the two postulates of special relativity. In the free particle case, our transformation theory generates a Poincaré group which fixes time (system proper-time). We prove that the Fushchych-Shtelen transformation is an element of our group, which fixes time for Maxwell’s equations. In the interaction case, our transformation theory allows us to avoid the no-interaction theorem. We show that the Santilli Isotopes appear naturally when interaction is turned on. 相似文献
9.
Tom Kennedy 《Journal of statistical physics》2010,140(3):409-426
Real-space renormalization group maps, e.g., the majority rule transformation, map Ising-type models to Ising-type models
on a coarser lattice. We show that each coefficient in the renormalized Hamiltonian in the lattice-gas variables depends on
only a finite number of values of the renormalized Hamiltonian. We introduce a method which computes the values of the renormalized
Hamiltonian with high accuracy and so computes the coefficients in the lattice-gas variables with high accuracy. For the critical
nearest neighbor Ising model on the square lattice with the majority rule transformation, we compute over 1,000 different
coefficients in the lattice-gas variable representation of the renormalized Hamiltonian and study the decay of these coefficients.
We find that they decay exponentially in some sense but with a slow decay rate. We also show that the coefficients in the
spin variables are sensitive to the truncation method used to compute them. 相似文献
10.
We formulate a Hamiltonian theory on the lattice including next-to-nearest neighbor fermion interactions. A canonical transformation is made to induce a momentum-dependent mass term. The meson spectrum is studied by using this Hamiltonian. The current algebra formula for the pion mass is derived. The ρ-ω mass ratio in the intermediate coupling region is in agreement with the experimental value. 相似文献
11.
We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation. 相似文献
12.
Sh. Mamedov 《The European Physical Journal C - Particles and Fields》2007,49(4):983-995
The unitary transformation which diagonalizes the squared Dirac equation in a constant chromomagnetic field is found. Applying
this transformation, we find the eigenfunctions of the diagonalized Hamiltonian, that describes the states with a definite
value of energy, and we call them energy states. It is pointed out that the energy states are determined by the color interaction
term of the particle with the background chromofield, and this term is responsible for the splitting of the energy spectrum.
We construct supercharge operators for the diagonal Hamiltonian that ensure the superpartner property of the energy states.
PACS 03.65.-w
An erratum to this article can be found at 相似文献
13.
Bob Rink 《Communications in Mathematical Physics》2001,218(3):665-685
The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct
a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This “Birkhoff–Gustavson
normal form” retains the symmetries of the original system and we show that in most cases this allows us to view the periodic
FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves
the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We
note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and
its special features are caused by a combination of special resonances and symmetries.
Received: 25 July 2000 / Accepted: 20 December 2000 相似文献
14.
The Heisenberg spin-S quantum antiferromagnet is studied near the large-spin limit, applying a new continuous unitary transformation which extends the usual Bogoliubov transformation to higher order in the 1/S-expansion of the Hamiltonian. This allows to diagonalize the bosonic Hamiltonian resulting from the Holstein-Primakoff representation
beyond the conventional spin-wave approximation. The zero-temperature flow equations derived from the extension of the Bogoliubov
transformation to order for the ground-state energy, the spin-wave velocity, and the staggered magnetization are solved exactly and yield results
which are in agreement with those obtained by a perturbative treatment of the magnon interactions.
Received: 19 March 1998 / Revised: 2 June 1998 / Accepted: 8 June 1998 相似文献
15.
Mei Yin 《Physica A》2013
We aim at an explicit characterization of the renormalized Hamiltonian after decimation transformation of a one-dimensional Ising-type Hamiltonian with a nearest-neighbor interaction and a magnetic field term. To facilitate a deeper understanding of the decimation effect, we translate the renormalization flow on the Ising Hamiltonian into a flow on the associated Markov chains through the Markov–Gibbs equivalence. Two different methods are used to verify the well-known conjecture that the eigenvalues of the linearization of this renormalization transformation about the fixed point bear important information about all six of the critical exponents. This illustrates the universality property of the renormalization group map in this case. 相似文献
16.
Zhen Wang 《International Journal of Theoretical Physics》2011,50(9):2666-2672
By introducing the four-level state ket-bra operators as atomic variables, we show that the Hamiltonian of a four-level system
with two lower levels and two top levels, which are respectively almost degenerate, interacting with four light fields through
double Λ configuration process, can be reformed as a standard Jaynes-Cummings Hamiltonian. Then the supersymmetric transformation
method can be employed to diagonalize the Hamiltonian. This approach may be generalized to tackle other atom-photon interaction
models since the supersymmetric transformation method is concise. 相似文献
17.
The exponential transformation, developed in an earlier paper [1], is applied to the Hamiltonian of a linear harmonic chain with a molecular defect. The resulting eigenvalue equation is solved for the localized frequency. A discussion of the renormalized in-band frequencies shows that in good approximation the entire Hamiltonian is diagonalized by a single transformation. This is of great advantage, since in the classical Lifshitz formalism each single frequency has to be evaluated separately. Furthermore, a simpler transformation is discussed, which is derived from an U-matrix formalism. Numerical results of the two transformations are given for a chain with 999 lattice points and compared with the exact values from the classical Lifshitz formalism. 相似文献
18.
We construct the two-component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. We obtain in this limit a new integrable system which, under a hodograph transformation, reduces to a coupled three-component system. We show how the Hamiltonian structure transforms under a hodograph transformation and study the properties of the model under a further reduction to a two-component system. 相似文献
19.