The TQ equation of the 8 vertex model for complex elliptic roots of unity

We extend our studies of the TQ equation introduced by Baxter in his 1972 solution of the 8 vertex model with parameter $\eta$ given by $2L\eta=2m_1K+im_2K'$ from $m_2=0$ to the more general case of complex $\eta.$ We find that there are several different cases depending on the parity of $m_1$ and $m_2$.Comment: 30 pages, LATE

Finite-dimensional reductions of the discrete Toda chain

The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well known discrete Painlev\'e equations $dP_{III}$, $dP_{V}$, $dP_{VI}$. Lax representations for these discrete Painlev\'e equations are found.Comment: Submitted to Jornal of Physics A: Math. Gen., 14 page

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty

Integrable flows in c=1 string theory

In these notes we review the method to construct integrable deformations of the compactified c=1 bosonic string theory by primary fields (momentum or winding modes), developed recently in collaboration with S. Alexandrov and V. Kazakov. The method is based on the formulation of the string theory as a matrix model. The flows generated by either momentum or winding modes (but not both) are integrable and satisfy the Toda lattice hierarchy.Comment: sect.1 extended and typos correcte

Influence of pathogenetic psychopharmacotherapy on duration of remissions at alcoholism at teenage age

As a result of complex clinical, psychological, neuropsychological, neurophysiological research of 110 teenagers, suffering from early alcoholism, it is established that in all cases signs of a residual organic psychosyndrome were defined. This was made for the optimization of drug abuse assistance, development of new cure methods and preventive health care. In the result of integrated clinical, psychological, neutropsychological, neurophysiological research of adolescent suffering from precocious alcoholism there was discovered that rod-shaped psychoorganic syndrome is a universal one for all of these observations. The genesis of epilepsy and the disturbance of functional interhemispheric interaction are the biological pathogenetic bases of this syndrome. The disturbance appears in the result of the residual organic lesion of temporal, parietal and occipital cerebral hemispheres. The anticonvulsants and the antiorganic therapy courses should be used for the patient treatment. The understanding of the above-stated mechanisms of formation and development of early alcoholism serves optimization of the medical-rehabilitation help and increase of duration of remissions.В результате комплексного клинического, психологического, нейропсихологического, нейрофизиологического исследования 110 подростков, страдающих ранним алкоголизмом, установлено, что во всех случаях определялись признаки резидуально-органического психосиндрома. Формирование органического поражения головного мозга обусловлено патогенными факторами, действующими на ранних этапах онтогенеза (в пре- и перинатальном периоде). Компенсация органически измененного мозга происходит за счет процесса эпилептизации (формирования гипергенераторных характеристик нейрона), играющей решающее значение в возникновении психопатологических синдромов резидуально-органического генеза. В связи с чем, эффективное лечение данной когорты больных подразумевает использование антиконвульсантов и средств нейрометаболической терапии. Понимание механизмов становления и развития раннего алкоголизма служит оптимизации лечебно-реабилитационной помощи и повышению длительности ремиссий

Psychosexual disorder at the adolescent suffering from alcohol addiction

During the present research clinical features of psychosexual frustration at 110 teenagers with alcoholic dependence are studied. Results testify that regular alcoholization negatively influences on the termination of prepubertal period and first half of puberty of psychosexual development. The sexuality transition period comes much earlier at the expense of exogenous harm stimulation. Alcoholic intoxication and regular alcoholization strengthen a sexual desire at teenagers that leads to increase in quantity of sexual contacts. The sexual desire also raises in a sober condition. Such sexual deviations as promiscuity, group sex supplement the list of the designated infringements. Regular alcoholization causes diserection, tardoejaculatory and unejaculatory syndromes at young men, anorgasmia at girls. At the young men, sexual dysfunctions arising in a sober condition, are impotence harbingers. The chronic alcoholic intoxication also promoted occurrence of infringements of psychosexual orientation and sexual deviation. Most often arose scopophilia and a narcissism with the subsequent masturbation.В ходе настоящего исследования были изучены клинические особенности психосексуальных расстройств у 110 подростков обоего пола с алкогольной зависимостью. В результате было установлено негативное влияние систематической алкоголизации на завершение препубертатного периода и становление первой половины пубертатного периодов психосексуального развития. Преждевременное становление сексуальности обусловлено стимуляцией мозговых структур экзогенным патогенным фактором. Алкогольное опьянение и систематическая алкоголизация усиливают половое влечение подростков, приводя к увеличению количества половых контактов. При зтом половое влечение повышается и в трезвом состоянии. Промискуитет, групповой секс дополняют перечень сексуальных девиаций. Систематическая алкоголизация обусловливает у юношей дисэрекционный, тардоэякуляторный и анэякуляторный синдромы, у девушек - аноргазмию. У юношей, возникающие в трезвом состоянии половые дисфункции, являются предвестниками импотенции. Хроническая алкогольная интоксикация приводила к частому возникновению феномена скопофилии и нарциссизма с последующей мастурбацией

Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with non-periodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.Comment: 15 pages, standard LaTe

The master T-operator for vertex models with trigonometric RR-matrices as classical tau-function

The construction of the master T-operator recently suggested in Alexandrov et al. (arXiv:1112.3310) is applied to integrable vertex models and associated quantum spin chains with trigonometric R-matrices. The master T-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. At the same time it turns out to be the tau-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the the same bilinear Hirota equations. The class of solutions of the Hirota equations that correspond to eigenvalues of the master T-operator is characterized and its relation to the classical Ruijsenaars-Schneider system of particles is discussed.Comment: 19 pages, for proceedings of the workshop "Classical and Quantum Integrable Systems" (Dubna, 23-27 January 2012), typos correcte

Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon

The raise and peel model of a one-dimensional fluctuating interface (model A) is extended by considering one source (model B) or two sources (model C) at the boundaries. The Hamiltonians describing the three processes have, in the thermodynamic limit, spectra given by conformal field theory. The probability of the different configurations in the stationary states of the three models are not only related but have interesting combinatorial properties. We show that by extending Pascal's triangle (which gives solutions to linear relations in terms of integer numbers), to an hexagon, one obtains integer solutions of bilinear relations. These solutions give not only the weights of the various configurations in the three models but also give an insight to the connections between the probability distributions in the stationary states of the three models. Interestingly enough, Pascal's hexagon also gives solutions to a Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few references are adde

Nested Bethe ansatz for "all" closed spin chains

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), U_q(gl(n)) or U_q(gl(m|n)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain. In particular, the case of indecomposable representations of superalgebras is studied. The construction extends and unifies the results already obtained for spin chains based on Y(gl(n)) or U_q(gl(n)) and for some particular super-spin chains. We give the Bethe equations and the form of the Bethe vectors. The case of gl(2|1), gl(2|2$ and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detailed.Comment: 30 pages; New section on indecomposable representations added and the case of gl(2|1), gl(2|2) and gl(4|4) superalgebras (that are related to AdS/CFT correspondence) is also detaile