相关论文: Equivalent Representations of Collective Hamiltoni…

We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…

We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic…

Equivalent guiding-center Hamiltonian theories are constructed based on higher-order Lie-transform perturbation methods. Higher-order guiding-center theories are distinguished on the basis of whether correction terms associated with…

It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…

We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…

We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…

Recently I proposed a new method for solving the pairing Hamiltonian with the pair-condensate wavefunction ansatz based on the Heisenberg equations of motion for the density matrix operators. In this work an improved version is given by…

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for…

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian - depending on quantum coupling and temperature - and classical-like expressions for the…

Two complementary representations of higher-order guiding-center theory are presented, which are distinguished by whether higher-order corrections due to magnetic-field nonuniformity appear in the guiding-center Poisson bracket or the…

We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…

The canonical Hamiltonian $H_C$ of the metric General Relativity is reduced to its natural form. The natural form of canonical Hamiltonian provides numerous advantages in actual applications to the metric GR, since the general theory of…

We consider powers of the absolute value of the characteristic polynomial of Haar distributed random orthogonal or symplectic matrices, as well as powers of the exponential of its argument, as a random measure on the unit circle minus small…

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…

Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…

We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the context of quasi-exactly solvable spectral problems. This Hamiltonian is expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical expressions…

While dealing in [1] with the supersymmetry of a tridiagonal Hamiltonian H, we have proved that its partner Hamiltonian H(+) also have a tridiagonal matrix representation in the same basis and that the polynomials associated with the…

We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded…

We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…