Related papers: Equivalent Hamiltonians
We describe a general method to identify exact, local parent Hamiltonians for trial states like quantum Hall or spin liquid states, which we have used extensively during the past decade. It can be used to identify exact parent Hamiltonians,…
Necessary and sufficient conditions are already known in the Hardy spaces of both the disc and the half plane for a composition operator to be an isometry, by Nordgren in the disc and by Chalendar and Partington in the half plane. All the…
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…
We investigate some questions on the construction of $\eta$ operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of $\eta$ operators starting from a known…
We propose asymmetric factorization method for supersymmetry involving complex operators. Model Hamiltonians satisfy supersymmetric energy conditions $E_{n}^{(+)}=E_{n+1}^{(-)}$; $E_{0}^{(-)}=0$.
If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way…
The characteristic polynomial of the effective Hamiltonian for a general model has been discussed. It is found that, compared with the associated energy eigenvalues, this characteristic polynomial generally has better analytical properties…
Analogue Hamiltonian simulation is a promising near-term application of quantum computing and has recently been put on a theoretical footing. In Hamiltonian simulation, a physical Hamiltonian is engineered to have identical physics to…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
We give two distinct infinite-Hamiltonian representations for the Riemann equation. One with first order Hamiltonian operators and another with third order-first order Hamiltonian operators. Both representations contain an arbitrary…
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…
Eigenvalues and eigenfunction of two-boson 2x2 Hamiltonians in the framework of the superalgebra osp(2,1) are determined by presenting a similarity transformation. The Hamiltonians include two bosons and one fermion have been transformed in…
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…
Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is…
Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogeneous Hamiltonian operators. The trios yield pairs of…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
If a reduced bivariate polynomial is quasi-homogeneous, then its discriminant is a monomial. Over fields of characteristic $0$, we show that if one adds another simple condition, this becomes an equivalence. We also give a third equivalent…