Related papers: Trace formulas for time periodic complex Hamiltoni…
We formulate Hamiltonian vector-like lattice gauge theory using the overlap formula for the spatial fermionic part, $H_f$. We define a chiral charge, $Q_5$ which commutes with $H_f$, but not with the electric field term. There is an…
The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good…
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
For the radial and one-dimensional Schr\"{o}dinger operator $H$ with growing potential $q(x)$ we outline a method of obtaining the trace identities - an asymptotic expansion of the Fredholm determinant $\mathrm{det}_{F}(H-\lambda I)$ as…
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
I discuss the connection between the Hamiltonian and path integral approaches for fermionic fields. I show how the temporal Wilson projection operators appear naturally in a lattice action. I also carefully treat the insertion of a chemical…
This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the…
This paper establishes trace-formulae for a class of operators defined in terms of the functional calculus for the Laplace operator on divergence-free vector fields with relative and absolute boundary conditions on Lipschitz domains in…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
Hamiltonian matrices appear in a variety or problems in physics and engineering, mostly related to the time evolution of linear dynamical systems as for instance in ion beam optics. The time evolution is given by symplectic transfer…
We introduce and investigate a number of fragments of propo- sitional temporal logic LTL over the flow of time (Z, <). The fragments are defined in terms of the available temporal operators and the structure of the clausal normal form of…
We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately…
Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may indeed cross, and as a result, the complex trajectories for such…
We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
We consider a Froehlich-type Hamiltonian on a hexagonal lattice. Aiming to describe nanotubes, we choose this 2-dimensional lattice to be periodic and to have a large extension in one (x) direction and a small extension in the other (y)…
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory…
Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a {\em probe energy}), we derive a formula for the Laplace time average of its expectation value up to…