In this paper, we study a linearized two-dimensional Euler equation. This equation decouples into infinitely many invariant subsystems. Each invariant subsystem is shown to be a linear Hamiltonian system of infinite dimensions. Another important invariant besides the Hamiltonian for each invariant subsystem is found and is utilized to prove an ‘‘unstable disk theorem’’ through a simple energy–C...

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 formula for an effective Hamiltonian generating the scattering operator of a general linear quantum network. Our formula shows how to compute the effective Ham...

We continue here the analysis of the previous paper of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canon-ical vacuum quantum gravity in the continuum. In this paper we derive the complete kernel, as well as a physical inner product on it, for a non-symmetric version of the Wheeler-DeWitt operator. We then deene a symmetric version of the Wheeler-De...

In this paper, we investigate the ϕ4 model with cutoffs. By introducing a spatial cutoff and momentum cutoff, total Hamiltonian is self-adjoint operator on boson Fock space. Under regularity conditions of obtain first order expansion non-degenerate ground state energy Hamiltonian.

Motivated by the fact that twice Fourier transform plays role of parity operator. We systematically study integral transforms in case $\mathcal{PT}$-symmetric Hamiltonian. First, we obtain a closed analytical formula for exponential general Using Segal-Bargmann transform, investigate effect on eigenfunctions original As an immediate application, comment holomorphic representation non-Hermitian ...

In this work we study how the infrared sector of the interaction Hamiltonian can affect the construction of the S matrix operator of QED in (2+1) dimensions.

Using a formalism developed by Polychronakos, we explicitly construct a set of invariants of the motion for the Haldane-Shastry SU(N) chain. Submitted to Physical Review Letters, PACS numbers: 75.10.Jm, 05.30.-d, 03.65.Ca † [email protected] ‡ [email protected] There have been several recent papers on the Haldane-Shastry model for spin chains and its SU(N) generalizat...

Time-dependent unitary transformations are used to study the Schrödinger equation for explicitly timedependent Hamiltonians of the form H(t) = ~ R(t) · ~ J , where ~ R is an arbitrary real vector-valued function of time and ~ J is the angular momentum operator. The solution of the Schrödinger equation for the most general Hamiltonian of this form is shown to be equivalent to the special case ~ ...

In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism invariant Hilbert space, which is both ...