Search results for "Ham"
showing 10 items of 2612 documents
Equivariant cohomology, Fock space and loop groups
2006
Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.
Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point
1985
We restrict ourselves to the stability problems considered in our lecture because the length of this paper is limited. In contrast to the lecture, however, we consider here not only area preserving mappings but a more general class of mappings.
The Period Isomorphism
2017
The aim of this section is to define well-behaved isomorphisms between singular and de Rham cohomology of algebraic varieties.
The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations
2004
Abstract Denote by Q H and Q R the Hamiltonian class and reversible class of quadratic integrable systems. There are several topological types for systems belong to Q H ∩ Q R . One of them is the case that the corresponding system has two heteroclinic loops, sharing one saddle-connection, which is a line segment, and the other part of the loops is an ellipse. In this paper we prove that the maximal number of limit cycles, which bifurcate from the loops with respect to quadratic perturbations in a conic neighborhood of the direction transversal to reversible systems (called in reversible direction), is two. We also give the corresponding bifurcation diagram.
Remark on integrable Hamiltonian systems
1980
An extension ton degrees of freedom of the fact is established that forn=1 the time and the energy constant are canonically conjugate variables. This extension is useful in some cases to get action-angle variables from the general solution of a given integrable Hamiltonian system. As an example the Delaunay variables are proved to be canonical.
Holomorphic de Rham Cohomology
2017
We are going to define a natural comparison isomorphism between algebraic de Rham cohomology and singular cohomology of varieties over the complex numbers with coefficients in \(\mathbb {C}\). The link is provided by holomorphic de Rham cohomology, which we study in this chapter.
Gibbs states, algebraic dynamics and generalized Riesz systems
2020
In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita-Takesaki theory in our context.
Near abelian profinite groups
2012
Abstract A compact p-group G (p prime) is called near abelian if it contains an abelian normal subgroup A such that G/A has a dense cyclic subgroup and that every closed subgroup of A is normal in G. We relate near abelian groups to a class of compact groups, which are rich in permuting subgroups. A compact group is called quasihamiltonian (or modular) if every pair of compact subgroups commutes setwise. We show that for p ≠ 2 a compact p-group G is near abelian if and only if it is quasihamiltonian. The case p = 2 is discussed separately.
Intertwining operators for non-self-adjoint hamiltonians and bicoherent states
2016
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some {\em minimal ingredients}. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.
Non-self-adjoint hamiltonians defined by Riesz bases
2014
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these Hamiltonians} can be factorized in terms of generalized lowering and raising operators.