Related papers: Eigensolutions of the kicked Harper model
We investigate classical-quantum correspondence for kicked Harper model for extremely small values of the Planck constant $\hbar$. In the asymmetric case a pure quantum state shows clear signature of classical diffusive as well as super…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Recent studies have established that, in addition to the well-known kicked Harper model (KHM), an on-resonance double kicked rotor model (ORDKR) also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard…
A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…
Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection…
We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant $\he$. We here show…
We present a microscopic theory of transport in quasi-periodically driven environments (`kicked rotors'), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of Planck's…
The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian…
We analyze the driven Harper model, which appears in the problem of tight-binding electrons in the Hall configuration (normal to the lattice plane magnetic field plus in-plane electric field). The presence of an electric field extends the…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant…
k:th power (amplitude-)squeezed states are defined as the normalized states giving equality in the Schroedinger-Robertson uncertainty relation for the real and imaginary parts of the k:th power of the one-mode annihilation operator.…
Finite rank perturbations $T=N+K$ of a bounded normal operator $N$ on a separable Hilbert space are studied thanks to a natural functional model of $T$; in its turn the functional model solely relies on a perturbation matrix/ characteristic…
We study multifractal properties in the spectrum of effective time-independent Hamiltonians obtained using a perturbative method for a class of delta-kicked systems. The evolution operator in the time-dependent problem is factorized into an…
We present here a complete description of the quantization of the baker's map. The method we use is quite different from that used in Balazs and Voros [BV] and Saraceno [S]. We use as the quantum algebra of observables the operators…
Kicked Harper operators and on-resonance double kicked rotor operators model quantum systems whose semiclassical limits exhibit chaotic dynamics. Recent computational studies indicate a striking resemblance between the spectrums of these…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the…
Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix} A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the…
We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…