Effective Hamiltonians for fastly driven many-body lattice systems

We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunnelling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to non-trivial processes such as single-particle density-dependent tunnelling, correlated pair hoppings, nearest neighbour interactions, etc. Some of these processes arise also in multiband lattice models, and are capable to give rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g. Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role

Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances

We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be satisfied. Correspondingly, phenomena of scattering on a resonance and capture into a resonance happen in the system. These phenomena lead to destruction of adiabatic invariance and to unlimited acceleration of the particle.Comment: 20 pages. Presented on School-Conference "Mathematics and Physics of Billiard-Like Systems" (Ubatuba, 2011). Accepted to Chao

Semiclassical Spectrum of Small Bose-Hubbard Chains: A Normal Form Approach

We analyze the spectrum of the 3-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance normal form theory. The derivation takes into account the 1:1 resonance between frequencies of a linearized classical system, and brings nonlinear terms into a corresponding normal form. The obtained expressions reproduce the exact low-energy spectrum of the system remarkably well even for a small number of particles N corresponding to fillings of just two particles per site. Such small fillings are often used in current experiments, and it is inspiring to get insight into this quantum regime using essentially classical calculations.Comment: Minor corrections to the coefficients of the effective Hamiltonian in Eqs 14,15,18,19. Figs 1,2 are slightly modified, correspondingl

Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings

We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a qualitatively new nonlinear phenomenon in a NLZ model which we propose to call {\em separated adiabatic tunnelling}Comment: Accepted for publication in Physical Review E; Several misprints are corrected; main results are emphasized in the end of Introduction (including finite conversion efficiency in Feshbach resonance passage due to geometric jump in the action); bibliography is extende

Partial reconstitution of cutaneous microvessels in long-term survivors after allogeneic bone marrow transplantation

BACKGROUND: Graft-versus-host disease (GVHD) is a major complication after allogeneic hematopoietic stem cell transplantation (HSCT) and skin is involved in acute and chronic disease. Immune-mediated vessel attack and subsequent microvessel loss have been observed in skin of patients with chronic GVHD. OBJECTIVES: To test whether long-term survivors (LTS) after allogeneic HSCT without cutaneous GVHD show signs of persistent vascular remodeling. METHODS: Microvessels in skin biopsies were investigated in a cohort of 32 LTS with a median follow-up of 17 years (range 11-26). Five were currently classified as having chronic GVHD other than skin involvement. RESULTS: LTS showed no significant difference in median microvessel density and relative vessel size distribution pattern compared to healthy controls. Past experience of GVHD and current status of chronic GVHD other than skin involvement had no impact on vessel density. In contrast, recipients with chronic cutaneous GVHD of sclerotic type and patients with lichen sclerosus have significant microvessel loss in the upper dermis. CONCLUSION: The complex therapy of allogeneic HSCT had no sustained effect on the microvascular architecture of LTS when clinicopathological evidence of cutaneous GVHD is absent. Microvascular remodeling as observed during chronic GVHD recovers completely after resolution of chronic cutaneous GVHD