Effective Hamiltonians for Rapidly Driven Many-Body Lattice Systems: Induced Exchange Interactions and Density-Dependent Hoppings.

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 tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving 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.

Intrinsic photoconductivity of ultracold fermions in optical lattices.

We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.

Directed transport in a classical lattice with a high-frequency driving.

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown by S. Flach and coworkers [Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptotic description of this phenomenon for the case of slow driving was developed by X. Leoncini and coworkers [Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using the canonical perturbation theory. An asymptotic formula is derived for the average drift velocity as a function of the system parameters and the driving law. We show that directed transport arises in an effective Hamiltonian that does not possess chaotic dynamics, thereby clarifying the relation between chaos and transport in the system. Sufficient conditions for transport are derived.

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 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.

Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates.

We discuss the dynamics of approximate adiabatic invariants in several nonlinear models being related to the physics of Bose-Einstein condensates (BECs). We show that the nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunneling, and BEC tunneling 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 nonlinear phenomenon in the NLZ model which we propose to call separated adiabatic tunneling.

Integrability, stability, and adiabaticity in nonlinear stimulated Raman adiabatic passage.

We study the dynamics of a two-color photoassociation of atoms into diatomic molecules via nonlinear stimulated Raman adiabatic passage process. The system has a famous counterpart in (linear) quantum mechanics, and has been discussed recently in the context of generalizing the quantum adiabatic theorem to nonlinear systems. Here we use another approach to study adiabaticity and stability in the system: we apply methods of classical Hamiltonian dynamics. We find nonlinear dynamical instabilities, cases of complete integrability, and improved conditions of adiabaticity.

Resonant phenomena in classical dynamics of three-body Coulomb systems.

We consider dynamics of a planar three-body Coulomb system similar to a hydrogen molecular ion (heavy-light-heavy particles). The system has three degrees of freedom. In the limit of infinitely heavy nuclei the system is reduced to the famous two-center problem which is integrable. When masses of heavy particles are finite, one degree of freedom in the Hamiltonian system corresponds to slow nuclei motion, while other two degrees of freedom correspond to fast electron motion. The averaging method predicts that actions of "fast" motions of the system with frozen nuclei are approximate integrals of the full system (adiabatic invariants). However, during slow evolution of the "heavy" subsystem certain resonance conditions can be satisfied. We study the phenomena of capture into resonances and scattering on resonances which can lead to destruction of adiabatic invariance in the system.

Transport in a slowly perturbed convective cell flow.

We study transport properties in a simple model of two-dimensional roll convection under a slow periodic (period of order 1/ varepsilon >>1) perturbation. The problem is considered in terms of conservation of the adiabatic invariant. It is shown that the adiabatic invariant is well conserved in the system. It results in almost regular dynamics on large time scales (of order approximately varepsilon (-3) ln varepsilon ) and hence, fast transport. We study both generic systems and an example having some symmetry. (c) 2002 American Institute of Physics.

Comment on "pi kinks in strongly ac driven sine-Gordon systems".

V. Zharnitsky, I. Mitkov, and N. Gronbech-Jensen [Phys. Rev. E 58, 1, R52 (1998)] found that pi kinks can propagate in strongly perturbed, directly driven rescaled sine-Gordon system provided that the parameters are chosen to make 2pi kink localization vanish. In this paper we would like to note that beside pi and 2pi kinks there can exist other kinklike solutions due to the fact that two unstable equilibria in the sine-Gordon phase emerging at a critical value of the drive amplitude are not necessarily separated by pi, to the contrary with the result of Zharnitsky, Mitkov, and Gronbech-Jensen. As a result, for the nondissipative system two one-parameter families of kink solutions exist that in the degenerate case become a one-parameter family of pi-kink solutions obtained in Zharnitsky, Mitkov, and Gronbech-Jensen. In the dissipative case velocity is selected for each of the two families of kink solutions by the balance between perturbations.

A novel role for VEGF in endocardial cushion formation and its potential contribution to congenital heart defects.

Normal cardiovascular development is exquisitely dependent on the correct dosage of the angiogenic growth factor and vascular morphogen vascular endothelial growth factor (VEGF). However, cardiac expression of VEGF is also robustly augmented during hypoxic insults, potentially mediating the well-established teratogenic effects of hypoxia on heart development. We report that during normal heart morphogenesis VEGF is specifically upregulated in the atrioventricular (AV) field of the heart tube soon after the onset of endocardial cushion formation (i.e. the endocardium-derived structures that build the heart septa and valves). To model hypoxia-dependent induction of VEGF in vivo, we conditionally induced VEGF expression in the myocardium using a tetracycline-regulated transgenic system. Premature induction of myocardial VEGF in E9.5 embryos to levels comparable with those induced by hypoxia prevented formation of endocardial cushions. When added to explanted embryonic AV tissue, VEGF fully inhibited endocardial-to-mesenchymal transformation. Transformation was also abrogated in AV explants subjected to experimental hypoxia but fully restored in the presence of an inhibitory soluble VEGF receptor 1 chimeric protein. Together, these results suggest a novel developmental role for VEGF as a negative regulator of endocardial-to-mesenchymal transformation that underlies the formation of endocardial cushions. Moreover, ischemia-induced VEGF may be the molecular link between hypoxia and congenital defects in heart septation.

Selective ablation of immature blood vessels in established human tumors follows vascular endothelial growth factor withdrawal.

Features that distinguish tumor vasculatures from normal blood vessels are sought to enable the destruction of preformed tumor vessels. We show that blood vessels in both a xenografted tumor and primary human tumors contain a sizable fraction of immature blood vessels that have not yet recruited periendothelial cells. These immature vessels are selectively obliterated as a consequence of vascular endothelial growth factor (VEGF) withdrawal. In a xenografted glioma, the selective vulnerability of immature vessels to VEGF loss was demonstrated by downregulating VEGF transgene expression using a tetracycline-regulated expression system. In human prostate cancer, the constitutive production of VEGF by the glandular epithelium was suppressed as a consequence of androgen-ablation therapy. VEGF loss led, in turn, to selective apoptosis of endothelial cells in vessels devoid of periendothelial cells. These results suggest that the unique dependence on VEGF of blood vessels lacking periendothelial cells can be exploited to reduce an existing tumor vasculature.

Apposition-dependent induction of plasminogen activator inhibitor type 1 expression: a mechanism for balancing pericellular proteolysis during angiogenesis.

Plasminogen-activator inhibitor type I (PAI-1), the primary inhibitor of urinary-type plasminogen activator, is thought to play an important role in the control of stroma invasion by both endothelial and tumor cells. Using an in vitro angiogenesis model of capillary extension through a preformed monolayer, in conjunction with in situ hybridization analysis, we showed that PAI-1 mRNA is specifically induced in cells juxtaposed next to elongating sprouts. To further establish that PAI-1 expression is induced as a consequence of a direct contact with endothelial cells, coculture experiments were performed. PAI-1 mRNA was induced exclusively in fibroblasts (L-cells) contacting endothelial cell (LE-II) colonies. Reporter gene constructs driven by a PAI-1 promoter and stably transfected into L-cells were used to establish that both mouse and rat PAI-1 promoters mediate apposition-dependent regulation. This mode of PAI-1 regulation is not mediated by plasmin, as an identical spatial pattern of expression was detected in cocultures treated with plasmin inhibitors. Because endothelial cells may establish direct contacts with fibroblasts only during angiogenesis, we propose that focal induction of PAI-1 at the site of heterotypic cell contacts provides a mechanism to negate excessive pericellular proteolysis associated with endothelial cell invasion.

Translation of vascular endothelial growth factor mRNA by internal ribosome entry: implications for translation under hypoxia.

Vascular endothelial growth factor (VEGF) is a hypoxia-inducible angiogenic growth factor that promotes compensatory angiogenesis in circumstances of oxygen shortage. The requirement for translational regulation of VEGF is imposed by the cumbersome structure of the 5' untranslated region (5'UTR), which is incompatible with efficient translation by ribosomal scanning, and by the physiologic requirement for maximal VEGF production under conditions of hypoxia, where overall protein synthesis is compromised. Using bicistronic reporter gene constructs, we show that the 1,014-bp 5'UTR of VEGF contains a functional internal ribosome entry site (IRES). Efficient cap-independent translation is maintained under hypoxia, thereby securing efficient production of VEGF even under unfavorable stress conditions. To identify sequences within the 5'UTR required for maximal IRES activity, deletion mutants were analyzed. Elimination of the majority (851 nucleotides) of internal 5'UTR sequences not only maintained full IRES activity but also generated a significantly more potent IRES. Activity of the 163-bp long "improved" IRES element was abrogated, however, following substitution of a few bases near the 5' terminus as well as substitutions close to the translation start codon. Both the full-length 5'UTR and its truncated version function as translational enhancers in the context of a monocistronic mRNA.

Vascular endothelial growth factor upregulation in human central retinal vein occlusion.

BACKGROUND AND OBJECTIVE: Vascular endothelial growth factor (VEGF), a key mediator of intraocular neovascularization, is triggered by hypoxia and has been shown in the eyes of animal models of central retinal vein occlusion (CRVO). However, there is little information on CRVO in humans, in particular, the identity of VEGF-producing cells. STUDY DESIGN: The study design was molecular localization of the site of VEGF production in the eyes of patients with CRVO. PARTICIPANTS: Ten formaldehyde solution-fixed and paraffin-embedded eyes removed surgically from patients with CRVO and neovascular glaucoma were studied. Five eyes with uveal melanoma and no neovascularization served as control specimens. METHODS: Thin whole-eye sections were hybridized in situ with a VEGF-specific probe to identify cells producing VEGF messenger RNA (mRNA). RESULTS: All ten eyes with CRVO showed evidence of intraretinal expression of VEGF mRNA. In all eyes, the inner nuclear layer showed VEGF-upregulated expression. Upregulation of VEGF mRNA was identified in four eyes in the ganglion cell layer and in two eyes with retinal detachment in the outer nuclear layer as well. CONCLUSIONS: The population of VEGF-producing retinal cells in each eye is likely to represent cells residing in ischemic regions of the retina. Hypoxia-induced VEGF is, most likely, the linking factor between retinal ischemia and iris and retinal neovascularization in CRVO.

[Current principles of diagnosis and surgical treatment of non-organ retroperitoneal tumors]. / Sovremennye printsipy diagnostiki i khirurgicheskogo lecheniia neorgannykh zabriushinnykh opukholei.

The data on surgical treatment of 455 patients operated on for primary and recurrent non-organ retroperitoneal tumors (NRT) are discussed. 64.2% of tumors were resected; postoperative lethality was 8.2%. Particular emphasis is placed on the complex nature of diagnosis and an algorithm of examination is suggested. The sequence of main procedures and stages are described; 43% of radical procedures were performed in combination with one another. NRTs tended to relapse and malignant tumors recurred most frequently within the first 18 months. In the course of 182 operations, 54.4% of NRTs were resected: postoperative lethality was 11.1%. The end results were determined by a number of factors, primarily, nature of tumor (benign or malignant), tumor process (primary or recurrent), tumor size and histological pattern. Because of the poor end results, surgical procedures should be improved and their range should be extended.

[Surgical treatment of adrenal gland tumors]. / K voprosu o khirurgicheskom lechenii opukholei nadpochechnikov.

The data on surgical treatment of 146 patients with adrenal gland malignancies as well as literature on the problem are discussed.

[Submerged esophago-intestinal anastomosis in surgical treatment of gastric cancer]. / Pogruzhnye pishchevodno-kishechnye anastomozy v khirurgicheskom lechenii raka zheludka.

The short-term results of 1,605 gastrectomies performed for stomach cancer, using different types of esophagoenterostomy, are discussed. Anastomotic leakage is the main criterion for a choice of the most optimal procedure of forming an anastomosis. The contribution of the first and second rows of sutures to leakage is evaluated. An analysis of data on anastomotic leakage incidence points to the advantages offered by application of submerged esophagus-related anastomosis. A new modification of procedure of formation of muffle-type of esophagoenterostomy is presented. Leakage was registered in 1.3% which was due to technical errors during surgery. The non-reflux properties of the anastomosis are emphasized, with particular emphasis on its reliability, good functional characteristics, simplicity and wide range of application. The clinical applications are described.

Loss of ovarian function promotes angiogenesis in human ovarian carcinoma.

We show here that elevated levels of gonadotropins (luteinizing hormone and follicle stimulating hormone), as found in menopause or after ovariectomy, promote growth of human ovarian carcinoma by induction of tumor angiogenesis. Human epithelial ovarian cancer tumors progressed faster in ovariectomized mice. This induced growth could be attributed to the elevated levels of gonadotropins associated with loss of ovarian function because direct administration of gonadotropins also was effective in promoting tumor progression in vivo. On the other hand, gonadotropins had no direct effect on the proliferation of human ovarian cancer cells in vitro. Using MRI, we demonstrated that ovariectomy significantly (P < 0.02) induces neovascularization of human ovarian carcinoma spheroids implanted in nude mice. Moreover, conditioned medium of gonadotropin-treated human ovarian carcinoma cells showed increased mitogenic activity to bovine endothelial cells, and this activity could be blocked by neutralizing antibodies against luteinizing hormone and against vascular endothelial growth factor. Accordingly, gonadotropin stimulation resulted in a dose-dependent-induced expression of vascular endothelial growth factor in monolayer culture as well as in the outer proliferating cells of human ovarian cancer spheroids. These results demonstrate the significance of the elevated levels of gonadotropins, as found in menopause and in all ovarian cancer patients, on the progression of ovarian cancer and could explain the protective effect of estrogen replacement therapy. Based on these results, we suggest that hormonal therapy aimed at lowering the circulating levels of gonadotropins may possibly prolong remission in ovarian cancer by extending tumor dormancy.

Rubeosis iridis in retinoblastoma. Histologic findings and the possible role of vascular endothelial growth factor in its induction.

PURPOSE: Iris neovascularization (rubeosis iridis) is a common finding in eyes harboring retinoblastoma. The purpose of the current study is to evaluate the histologic factors that may affect the development of rubeosis iridis in eyes with retinoblastoma and to examine whether vascular endothelial growth factor (VEGF), a hypoxia-induced angiogenic factor, is produced by hypoxic retinoblastoma and retinal cells in these eyes. MATERIALS AND METHODS: One hundred eighty-one enucleated eyes containing retinoblastoma were the source for the current study. Histologic slides were evaluated for the presence and degree of rubeosis iridis as well as for other histologic factors. Univariate and multivariate statistical analyses were performed to find a correlation between rubeosis iridis and the other histologic factors. Eight of the eyes underwent in situ hybridization with a specific VEGF mRNA probe to locate tumor and retinal cells that may produce this hypoxia-induced angiogenic factor. RESULTS: The amount of tumor necrosis as well as choroidal and optic nerve invasion was found to be one of the most important factors that correlated with the presence and degree of rubeosis iridis in the examined eyes. All eight eyes that underwent in situ hybridization analysis showed strong signals of VEGF mRNA in retinoblastoma cells around necrotic regions and in the outer nuclear layers in areas of detached retina. CONCLUSIONS: There exists an association between rubeosis iridis and histologic factors found in advanced stages of retinoblastoma, especially the amount of tumor necrosis. Vascular endothelial growth factor may well be an angiogenic factor that is secreted by the hypoxic retinoblastoma and retinal cells and, reaching the iris, causes (presumably in collaboration with other factors) rubeosis iridis.

Upregulated expression of vascular endothelial growth factor in proliferative diabetic retinopathy.

AIMS/BACKGROUND: Vascular endothelial growth factor (VEGF) is a hypoxia induced angiogenic factor. Recent studies have shown that high levels of VEGF accumulate in the vitreous of patients with proliferative diabetic retinopathy (PDR). The purpose of the present study was to identify the retinal cells that upregulate VEGF expression in human PDR patients representing progressive stages of retina deterioration. METHODS: Thirteen formalin fixed and paraffin embedded enucleated eyes with PDR were used (eyes were enucleated because of being blind and painful as a result of neovascular glaucoma). Thin retina sections were hybridised in situ with a VEGF specific probe, to identify cells producing VEGF mRNA. RESULTS: All eyes with PDR showed upregulated expression of VEGF mRNA, specifically in the cells of the neurosensory retina. VEGF expression was upregulated in all three nuclear layers--namely, the ganglion cell layer, the inner nuclear layer, and the outer nuclear layer. However, in each patient, VEGF producing cells were mostly distributed in a different layer, or even confined to a specific region in that layer. For example, expression by the outer nuclear layer was mostly detected in detached (presumably hypoxic) regions of the retina. CONCLUSIONS: Progression of PDR is distinguished by a sustained, upregulated expression of VEGF by the neurosensory retina. Cells in all retina layers can potentially contribute to augmented VEGF production. The restricted population of VEGF producing cells in each case is likely to represent cells residing in ischaemic regions of the retina. Thus, VEGF may function as a linking factor between retinal ischaemia and PDR associated neovascularisation.