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1.
We address the existence of traveling single-humped localized solutions in the spatially discrete nonlinear Schrödinger (NLS) equation. A mathematical technique is developed for analysis of persistence of these solutions from a certain limit in which the dispersion relation of linear waves contains a triple zero. The technique is based on using the Implicit Function Theorem for solution of an appropriate differential advance-delay equation in exponentially weighted spaces. The resulting Melnikov calculation relies on a number of assumptions on the spectrum of the linearization around the pulse, which are checked numerically. We apply the technique to the so-called Salerno model and the translationally invariant discrete NLS equation with a cubic nonlinearity. We show that the traveling solutions terminate in the Salerno model whereas they generally persist in the translationally invariant NLS lattice as a one-parameter family of solutions. These results are found to be in a close correspondence with numerical approximations of traveling solutions with zero radiation tails. Analysis of persistence also predicts the spectral stability of the one-parameter family of traveling solutions under time evolution of the discrete NLS equation.  相似文献   

2.
The properties of translationally invariant kinks in two discrete ϕ4 models are compared with those of the kinks in a classical discrete model. The translationally invariant kink solutions can be found randomly with respect to the lattice sites, i.e., their Peierls–Nabarro potential is exactly equal to zero. It is shown that these solutions have a Goldstone mode, that is, they can move along the lattice at vanishingly small velocities. Thus, the translationally invariant kink is not trapped by the lattice and can be accelerated by an arbitrary small external field and, having an increased mobility, can transfer a range of physical quantities: matter, energy, momentum, etc.  相似文献   

3.
A problem posed     
E. T. Jaynes' resolution of Bertrand's paradox in terms of invariance principles is criticized. An experimental setup is considered which generates general solutions to Bertrand's problem by rotating a line around a point a distancer+d from a circle of radiusr. The general solution obtained is neither translationally nor scale invariant, but depends on the value ofr/d. Only in the limitr/d » 0, when the line is just translating across the circle, is the distribution translationally invariant and scale invariant. In this limiting case the distribution found is just that obtained by Jaynes.  相似文献   

4.
We propose and solve exactly the Schrödinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type [1] and additional non translationally invariant four-body potentials. We also generalize and solve exactly this problem in any D-dimensional space by providing full eigensolutions and the corresponding energy spectrum. We discuss the domain of the coupling constant where the irregular solutions becomes physically acceptable.  相似文献   

5.
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems in 1D. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest-neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.  相似文献   

6.
The boson transformation, which allows the construction of spontaneously broken solutions with space and/or time-dependent vacuum directly from the translationally invariant ones, is examined in the context of the Higgs mechanism. Both the Lorentz and the radiation gauge are treated in detail. The classical vortex solution is derived by fully quantum field theoretical considerations. The general form of the vortex solution is presented, and various special cases of interest are examined in detail.  相似文献   

7.
For translationally shape invariant potentials, the exact quantization rule proposed by Ma and Xu results from the exactness of the modified JWKB quantization condition proved by Barclay. We propose here a very direct alternative way to calculate the appropriate correction for the whole class of translationally shape invariant potentials.  相似文献   

8.
It is shown that the pressure is a strictly convex function of the translationally invariant interactions (under certain mild restrictions on the long-range part of these interactions) for classical and quantum lattice systems, by demonstrating that two distinct interactions can never lead to the same translationally invariant equilibrium state. This generalizes a previous result that the pressure is a continuous function of density at fixed temperature.  相似文献   

9.
Gregory and Laflamme showed that certain nonextremal black strings (and p-branes) are unstable to linearized perturbations. It is widely believed that this instability will cause the black string horizon to classically pinch off and then quantum mechanically separate, resulting in higher dimensional black holes. We argue that this cannot happen. Under very mild assumptions, classical event horizons cannot pinch off. Instead, they settle down to new static black string solutions which are not translationally invariant along the string.  相似文献   

10.
We study certain quantum spin systems which are equivalent to stochastic Ising models. We show that any translationally invariant quantum ground state is given by integration of Gibbs measure. The existence of mass gap is shown to be the same as exponentially fast convergence of stochastic models to invariant states.  相似文献   

11.
We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in zeta/s near Tc. For constructions that exhibit a smooth crossover, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.  相似文献   

12.
13.
We investigate the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. We find that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the charge-density profile of translationally invariant states. The resulting phase diagram includes many of the stable odd-denominator states and also a novel fractional quantum Hall state at lowest half-filled Landau level. The collective modes evaluated at and at reveal soft modes in between the translationally invariant states in the phase diagram. 1997 Elsevier Science B.V. All rights reserved.  相似文献   

14.
We develop a new approach to build the eigenfunctions of a translationally shape invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We give explicit formulas for all the eigenstates, their specific form depending on the Barclay-Maxwell class to which the considered potential belongs.  相似文献   

15.
We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for layers that are translationally invariant in plane so that properties only vary perpendicular to the planes. Physical quantities like spin density, spin current, and spin-transfer torque are calculated directly from the distribution function. We illustrate our solution method with a systematic study of the spin-transfer torque in a spin valve as a function of its geometry. The results agree with a hybrid circuit theory developed by Slonczewski for geometries typical of those measured experimentally.  相似文献   

16.
We show that at low temperature an Ising spin system with antiferromagnetic interaction in a small enough external magnetic field has only one translationally invariant state.  相似文献   

17.
We investigate low temperature properties of an Ising ferromagnet when the nearest neighbour coupling constant is dominant. We show that all the translationally invariant equilibrium states are a superposition of only two extremal states.  相似文献   

18.
We prove that ground states of quantum spin systems are characterized by a principle of minimum local energy and that translationally invariant ground states are characterized by the principle of minimum energy per unit volume.  相似文献   

19.
We formulate local thermodynamical stability conditions for states of quantum lattice systems, and show that these conditions are implied by, and in the case of translationally invariant states equivalent to, those of Kubo-Martin-Schwinger (KMS).  相似文献   

20.
We provide a detailed study of the general structure of translationally invariant two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. We show that they can be understood in terms of the homology of string operators that carry a certain topological charge. In subsystem codes, two dual kinds of charges appear. We prove that two non-chiral codes are equivalent under local transformations iff they have isomorphic topological charges. Our approach emphasizes local properties over global ones.  相似文献   

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