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1.
A class of lump solutions of(2+1)-dimensional Boussinesq equation are obtained with the help of Maple by using Hirota bilinear method.Some contour plots with different determinant values are sequentially made to show that the corresponding lump solution tends to zero when the determinant approaches zero.The particular lump solutions with specific values of the involved parameters are plotted,as illustrative examples. 相似文献
2.
For the integrable couplings of Ablowitz-Kaup-Newell-Segur(ICAKNS) equations, N-fold Darboux transformation(DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the(4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae,the determinant expressions of N-transformed new solutions p~([N ]), q~([N ]), r~([N ])and s~([N ])are generated by this N-fold DT.Furthermore, when the reduced conditions q =-p*and s =-r*are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schr?dinger(ICNLS) equations.Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example. 相似文献
3.
Jan Finjord 《Nuclear Physics B》1983,222(3):507-515
The fermionic determinant is expanded in powers of the oscillations around a semiclassical background gluon field. In the quadratic approximation, with a translation invariant (anti)self-dual background SU(2) gluon field, the changes of the zero eigenvalues are investigated in a perturbative approximation. Subtracting the field-idependent contributions, the eigenvalue of the “color-longitudinal” zero mode is unchanged while those of the “color-transverse” zero modes get positive shifts, suggesting a further stabilization of the gluonic oscillations. 相似文献
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使用矩阵光学方法研究了非对称光学系统的矩阵分解和等效变换。将Arsenault提出的分解方法推广应用于分块矩阵行列式为零的4×4矩阵的分解,并以用于光束对称化的光学系统为例说明该方法的应用。 相似文献
6.
Junehyuk Jung 《Communications in Mathematical Physics》2016,342(2):603-614
The topological entropy htop of a continuous piecewise monotone interval map measures the exponential growth in the number of monotonicity intervals for iterates of the map. Milnor and Thurston showed that exp(–htop) is the smallest zero of an analytic function, now coined the Milnor–Thurston determinant, that keeps track of relative positions of forward orbits of critical points. On the other hand exp(htop) equals the spectral radius of a Ruelle transfer operator L, associated with the map. Iterates of L keep track of inverse orbits of the map. For no obvious reason, a Fredholm determinant for the transfer operator has not only the same leading zero as the M–T determinant but all peripheral (those lying in the unit disk) zeros are the same. The purpose of this note is to show that on a suitable function space, the dual of the Ruelle transfer operator has a regularized determinant, identical to the Milnor–Thurston determinant, hereby providing a natural explanation for the above puzzle. 相似文献
7.
We obtain a closed representation for the QCD2 fermion determinant, euclidean Green functions and induced current in generic external fields. In the absence of zero modes the results are representable as sums over tree diagrams which as we show, can also be obtained from the original Feynman perturbation series via resummation and integration over loop variables. We also investigate the modifications due to the presence of zero modes. 相似文献
8.
A determinant (permanent) of plane waves for N fermions (bosons) in their lowest-energy state, and a determinant (permanent) of spatially-localized, nonoverlapping, single-particle functions are used to determine conditions on the short-ranged, square-well repulsive plus Yukawa attractive, two-body potential for which the spatially homogeneous or periodic particle-density states are energetically preferred. A considerable region in the coupling parameter-density plane is found where “crystalline” solutions are preferred. In particular, for purely repulsive forces, the low-density region for which the “fluid” solution is lowest shrinks to zero in the limit of infinitely repulsive cores, but faster for bosons than fermions. Inclusion of attractive forces is seen not to alter qualitatively the main results. 相似文献
9.
The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor 总被引:1,自引:0,他引:1
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Based on a general model of Brownian motors, the Onsager
coefficients and generalized efficiency of a thermal Brownian motor
are calculated analytically. It is found that the Onsager
reciprocity relation holds and the Onsager coefficients are not
affected by the kinetic energy change due to the particle's motion.
Only when the heat leak in the system is negligible can the
determinant of the Onsager matrix vanish. Moreover, the influence of
the main parameters characterizing the model on the generalized
efficiency of the Brownian motor is discussed in detail. The
characteristic curves of the generalized efficiency varying with
these parameters are presented, and the maximum generalized
efficiency and the corresponding optimum parameters are determined.
The results obtained here are of general significance. They are used
to analyze the performance characteristics of the Brownian motors
operating in the three interesting cases with zero heat leak,
zero average drift velocity or a linear response relation, so that
some important conclusions in current references are directly
included in some limit cases of the present paper. 相似文献
10.
Eckhard Kreisel 《Annalen der Physik》1988,500(8):546-550
If in Antoci's solution [7] of Einstein-Schrödingers unified systems of equations the spacetime is equipped with Diraec's string topology, then the solution fulfills everywhere the Einstein-Schrödinger equations and the quark charges are of topological origin, For the pseudo-Hermitian theory the zero of the determinant of the metric is considered. 相似文献
11.
J.G. Papastavridis 《Journal of sound and vibration》1982,80(4):447-459
Hamilton's principle is applied to analyze the problem of the stability of equilibrium of a discrete, holonomic, and scleronomic mechanical system under conservative and non-conservative (position and/or velocity dependent) forces. At the stability limit, the vanishing of the second order terms (in the deviations from equilibrium) of the total action change functional leads to the condition that the matrix of a certain quadratic form be singular; this yields the eigenvalue (frequency-load) curve. The flutter loads follow by setting the frequency derivative of the determinant of this matrix equal to zero; the energetic interpretation of this latter is also given. When the non-conservative forces go to zero it is shown that one recovers the well-known discrete conservative system stability criterion. An application follows, and finally in an Appendix various relevant time-integral equalities are summarized and interpreted. 相似文献
12.
We analyse the physical constraints of the higher derivative Chern–Simons gauge model by means of Faddeev–Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev–Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac–Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations. 相似文献
13.
In this paper, we construct the Darboux transformation (DT) for the reverse-time integrable nonlocal nonlinear Schrödinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions. Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula. 相似文献
14.
We show that in the microscopic domain of QCD (also known as the domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for micro相似文献
15.
Eckhard Kreisel 《Annalen der Physik》1980,492(4):301-311
Einstein's Field Theory with Teleparallelism and Dirac's Elektrodynamics. III (Static, Spherically Symmetric Solution of the Approximated Field Equations) The static, spherially symmetric solution of the equation of gravitation, considered by Treder [1] and Kreisel [2] and connecting the electromagnetic potential by the Dirac-gauge with the time-like tetrad, is given for the case of small contributions of the space-like tetrads, which corresponds to Einstein-Dirac's electrodynamics. The threedimensional spaces of the solution are two-bladed. The two blades are connected by a wormhole. The solution has a zero of the determinant the metric in the second blade at r = ∞. Therefore the manifold is geodesically incomplete. 相似文献
16.
We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block of Lneighboring spins at zero temperature and of an infinite system. We represent the entropy in terms of a Toeplitz determinant and calculate the asymptotic analytically. We derive the first two terms of the asymptotic decomposition. Interestingly, these two terms of decomposition clearly show a length scale related to the field h. 相似文献
17.
《Nuclear Physics B》1986,266(2):309-356
We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling. 相似文献
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The N-fold Darboux transformation(DT) T_n~([N]) of the nonlinear self-dual network equation is given in terms of the determinant representation. The elements in determinants are composed of the eigenvalues λ_j(j = 1, 2..., N)and the corresponding eigenfunctions of the associated Lax equation. Using this representation, the N-soliton solutions of the nonlinear self-dual network equation are given from the zero "seed" solution by the N-fold DT. A general form of the N-degenerate soliton is constructed from the determinants of N-soliton by a special limit λ_j →λ_1 and by using the higher-order Taylor expansion. For 2-degenerate and 3-degenerate solitons, approximate orbits are given analytically,which provide excellent fit of exact trajectories. These orbits have a time-dependent "phase shift", namely ln(t~2). 相似文献
20.
We discuss the mathematical picture of anomalies. By solving the Dirac equation in the background of non-trivial families of gauge connections, we show explicitly the interplay between spectral flows, zero modes of the Dirac operator and projective representations of the gauge group, and the existence of both perturbative and non-perturbative anomalies. We give an explicit expression for the fermion determinant for chiral QCD in two dimensions when an anomaly is present. 相似文献