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

The thalamic low-threshold Ca2+ potential: a key determinant of the local and global dynamics of the slow (<1 Hz) sleep oscillation in thalamocortical networks

During non-rapid eye movement sleep and certain types of anaesthesia, neurons in the neocortex and thalamus exhibit a distinctive slow (<1 Hz) oscillation that consists of alternating UP and DOWN membrane potential states and which correlates with a pronounced slow (<1 Hz) rhythm in the electroencephalogram. While several studies have claimed that the slow oscillation is generated exclusively in neocortical networks and then transmitted to other brain areas, substantial evidence exists to suggest that the full expression of the slow oscillation in an intact thalamocortical (TC) network requires the balanced interaction of oscillator systems in both the neocortex and thalamus. Within such a scenario, we have previously argued that the powerful low-threshold Ca2+ potential (LTCP)-mediated burst of action potentials that initiates the UP states in individual TC neurons may be a vital signal for instigating UP states in related cortical areas. To investigate these issues we constructed a computational model of the TC network which encompasses the important known aspects of the slow oscillation that have been garnered from earlier in vivo and in vitro experiments. Using this model we confirm that the overall expression of the slow oscillation is intricately reliant on intact connections between the thalamus and the cortex. In particular, we demonstrate that UP state-related LTCP-mediated bursts in TC neurons are proficient in triggering synchronous UP states in cortical networks, thereby bringing about a synchronous slow oscillation in the whole network. The importance of LTCP-mediated action potential bursts in the slow oscillation is also underlined by the observation that their associated dendritic Ca2+ signals are the only ones that inform corticothalamic synapses of the TC neuron output, since they, but not those elicited by tonic action potential firing, reach the distal dendritic sites where these synapses are located

Renormalization the quantum field model of particle interaction

The model simulates the interaction of abstract entities distinguished in a physical experiment and denoted as particles. Empirical data results in the non-hermitian anti-symmetric matrix of particle relationship. The real and imaginary parts of the matrix correspond to symmetric and asymmetric coupling of particles. The relationship matrix evolves to multiplication of pure defined hermitian metric tensor and curvature vector. The real spectrum of metric tensor extended into the complex space with invariant spectrum power results in renormalized non-singular quantum field model of particle interaction.Рассматривается модель взаимодействия абстрактных сущностей, различимых в физическом эксперименте и названных частицами. Эмпирические данные представлены в форме неэрмитовой антисимметрической матрицы взаимодействия частиц. Вещественные и мнимые элементы матрицы соответствуют симметрической и асимметрической составляющим взаимодействующей пары частиц. Матрица взаимодействия приведена к произведению слабо обусловленного эрмитового метрического тензора на вектор кривизны. Вещественный спектр метрического тензора расширен в комплексную область с условием инвариантности мощности спектра, в результате чего получена ренормализованная несингулярная квантово-полевая модель взаимодействия частиц.Розглянуто модель взаємодії абстрактних сутностей, помітних у фізичному експерименті і названих частками. Емпіричні дані представлені у вигляді неермітової антисиметричної матриці взаємодії часток. Дійсні та уявні елементи матриці відповідають симетричній та асиметричній складовим взаємодіючої пари часток. Матриця взаємодії приведена к добутку слабо обумовленого метричного тензора на вектор кривизни. Дійсний спектр метричного тензора розширено у комплексну область за умови інваріантності потужності спектру, в результаті чого отримано ренормалізовану несингулярну квантово-польову модель взаємодії часток