Related papers: Recursive Generation of Isochronous Hamiltonian Sy…
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple…
Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
An algorith to count, or alternatively generate, all k-element transversals of a set system is presented and compared with three known methods. For special cases it works in output-linear time.
A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has…
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…
We show how to engineer an extensive range of non-linear Hamiltonians for a nano-mechanical resonator. The technique requires only a time dependent drive applied to a Cooper-pair box or second oscillator to which the nano-resonator is…
We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated…
We propose a novel approach to the generation of electromagnetic oscillations by means of a low-frequency pumping of two coupled linear oscillators. A theory of such generation mechanism is proposed, and its feasibility is demonstrated by…
We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…
We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…
This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Many combinatorial optimization problems can be mapped to finding the ground states of the corresponding Ising Hamiltonians. The physical systems that can solve optimization problems in this way, namely Ising machines, have been attracting…
We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…
We consider the deterministic generation of entangled multi-qubit states by the sequential coupling of an ancillary system to initially uncorrelated qubits. We characterize all achievable states in terms of classes of matrix product states…
This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…
A collective model is proposed to describe the chiral rotation and vibration and applied to a system with one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole coupled to a triaxial rigid rotor. The collective Hamiltonian is…
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do not have ground states that are the graph states needed in measurement-based quantum computation. Various highly-entangled many-body states have been suggested as a…