Quasi-equilibria in reduced Liouville spaces.
Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon
2012-06-14
The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.
Symmetry-adapted Liouville space. Pt. 7
Temme, F.P.
1990-01-01
In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over vertical strokekqv>> operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such (k i = 1) nuclear spin clusters. The SU2 X S n group provides the essential mappings and the form of H carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced S n -symmetry. (orig.)
Liouville's theorem and phase-space cooling
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
Connections of the Liouville model and XXZ spin chain
Faddeev, Ludvig D.; Tirkkonen, Olav
1995-02-01
The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with non-trivial spectral-parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe ansatz equations for Liouville theory, by the methods of the algebraic Bethe ansatz. Using the string picture of excited Bethe states, the lattice Liouville Bethe equations are mapped to the corresponding spin- {1}/{2} XXZ chain equations. The well developed theory of finite-size corrections in spin chains is used to deduce the conformal properties of the lattice Liouville Bethe states. The unitary series of conformal field theories emerge for Liouville couplings of the form γ = πν/( ν + 1), corresponding to root of unity XXZ anisotropies. The Bethe states give the full spectrum of the corresponding unitary conformal field theory, with the primary states in the Kač table parameterized by a string length K, and the remnant of the chain length mod ( ν + 1).
Connections of the Liouville model and XXZ spin chain
Faddeev, L.D.; Tirkkonen, O.
1995-01-01
The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with non-trivial spectral-parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe ansatz equations for Liouville theory, by the methods of the algebraic Bethe ansatz. Using the string picture of excited Bethe states, the lattice Liouville Bethe equations are mapped to the corresponding spin-1/2 XXZ chain equations. The well developed theory of finite-size corrections in spin chains is used to deduce the conformal properties of the lattice Liouville Bethe states. The unitary series of conformal field theories emerge for Liouville couplings of the form γ= πν/(ν+1), corresponding to root of unity XXZ anisotropies. The Bethe states give the full spectrum of the corresponding unitary conformal field theory, with the primary states in the Kac table parameterized by a string length K, and the remnant of the chain length mod (ν+1). (orig.)
Symmetry-adapted Liouville space. Pt. 8
Temme, F.P.
1990-01-01
A generalized hierarchy over lexical weight-sets is shown to provide significant insight into the structure of identical higher I i spin clusters under the S n /SO(3) dual groups. The use of combinatorial S n word-lengths allows one to derive the dual irreps directly from the combinatorics inherent in the adapted spin space. These advantages arise from the intimate connections between the scalar invariants of Cayley algebra over a field and their lexical combinatorics over vertical strokeI, Σ i M i , ()> space, which itself is a consequence of the S n -group representational algebra. By taking the highest SO(3) weight as the lexical origin, the calculations become recursive over all further expansions of the spin space, i.e., arising from an enhanced magnitude for the component nuclear spins, I i . The method over Hilbert space for spin clusters of I i ≤ 9/2 is more direct than those associated with unitary group algebras; in addition, the cogent beauty of combinatorial concepts derived from Cayley algebra deserves wider recognition in the physical sciences. (orig.)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Teschner, J.
2010-05-01
It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,ε 1 ,ε 2 ;q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R 4 which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)
Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie
2010-05-15
It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,{epsilon}{sub 1},{epsilon}{sub 2};q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R{sup 4} which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)
Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
Grinberg, H.
1983-11-01
The projection operator method of Zwanzig and Feshbach is used to construct the time-dependent field operators in the interaction picture. The formula developed to describe the time dependence involves time-ordered cosine and sine projected evolution (memory) superoperators, from which a master equation for the interaction-picture single-particle Green's function in a Liouville space is derived. (author)
Phase space representations for spin23
Polubarinov, I.V.
1991-01-01
General properties of spin matrices and density ones are considered for any spin s. For spin 2 3 phase space representations are constructed. Representations, similar to the Bell one, for the correlator of projections of two spins 2 3 in the singlet state are found. Quantum analogs of the Bell inequality are obtained. 14 refs
Super-Liouville — double Liouville correspondence
Hadasz, Leszek; Jaskólski, Zbigniew
2014-05-01
The AGT motivated relation between the tensor product of the = 1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.
Super-Liouville — double Liouville correspondence
Hadasz, Leszek; Jaskólski, Zbigniew
2014-01-01
The AGT motivated relation between the tensor product of the N=1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.
Super-Liouville — double Liouville correspondence
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,W. Reymonta 4, 30-059 Kraków (Poland); Jaskólski, Zbigniew [Institute of Theoretical Physics, University of Wrocław,pl. M. Borna 1, 95-204 Wrocław (Poland)
2014-05-27
The AGT motivated relation between the tensor product of the N=1 super-Liouville field theory with the imaginary free fermion (SL) and a certain projected tensor product of the real and the imaginary Liouville field theories (LL) is analyzed. Using conformal field theory techniques we give a complete proof of the equivalence in the NS sector. It is shown that the SL-LL correspondence is based on the equivalence of chiral objects including suitably chosen chiral structure constants of all the three Liouville theories involved.
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
La, H.
1992-01-01
A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint
Liouville action in cone gauge
Zamolodchikov, A.B.
1989-01-01
The effective action of the conformally invariant field theory in the curved background space is considered in the light cone gauge. The effective potential in the classical background stress is defined as the Legendre transform of the Liouville action. This potential is tightly connected with the sl(2) current algebra. The series of the covariant differential operators is constructed and the anomalies of their determinants are reduced to this effective potential. 7 refs
Schomerus, Volker; Suchanek, Paulina; Univ. of Wroclaw
2012-10-01
N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1 vertical stroke 2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bozonization.
Spin Hall effect on a noncommutative space
Ma Kai; Dulat, Sayipjamal
2011-01-01
We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V 1 (r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, σ=ρθ (ρ is the electron concentration, θ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.
Time Evolution Of The Wigner Function In Discrete Quantum Phase Space For A Soluble Quasi-spin Model
Galetti, D
2000-01-01
Summary: The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with an $SU(2)$-based semiclassical continuous approach to the Lipkin model is also presented.
Liouville quantum gravity on complex tori
David, François [Institut de Physique Théorique, CNRS, URA 2306, CEA, IPhT, Gif-sur-Yvette (France); Rhodes, Rémi [Université Paris-Est Marne la Vallée, LAMA, Champs sur Marne (France); Vargas, Vincent [ENS Paris, DMA, 45 rue d’Ulm, 75005 Paris (France)
2016-02-15
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. The difference is here that the moduli space for complex tori is non-trivial. Modular properties of LQFT are thus investigated. This allows us to integrate the LQFT on complex tori over the moduli space, to compute the law of the random Liouville modulus, therefore recovering (and extending) formulae obtained by physicists, and make conjectures about the relationship with random planar maps of genus one, eventually weighted by a conformal field theory and conformally embedded onto the torus.
L-1 constraint in Liouville gravity
Kitazawa, Y.
1992-01-01
In this paper, the authors study recursion relations among the amplitudes which involve discrete states in c = 1 Liouville gravity on the sphere. The authors find that the spin J = 1/2 discrete state gives rise to the L -1 type recursion relation. Multiple point correlation functions are determined recursively from fewer point functions by this recursion relation. The authors further point out that the analogs of J = 1/2 state exist in c -1 type recursion relation
Higher spin currents in orthogonal Wolf space
Ahn, Changhyun; Paeng, Jinsub
2015-01-01
For the N=4 superconformal coset theory by ((SO(N+4))/(SO(N)×SU(2)))×U(1) (that contains an orthogonal Wolf space) with N = 4, the N=2 WZW affine current algebra is obtained. The 16 generators (or 11 generators) of the large N=4 linear (or nonlinear) superconformal algebra are described by these WZW affine currents explicitly. Along the line of large N=4 holography, the extra 16 currents with spins (2,(5/2),(5/2),3), ((5/2),3,3,(7/2)), ((5/2),3,3,(7/2)), and (3,(7/2),(7/2),4) are obtained in terms of the WZW affine currents. The lowest spin of this N=4 multiplet is two rather than one, which is for a unitary Wolf space. The operator product expansions between the above 11 currents and these extra 16 higher spin currents are found explicitly. (paper)
Ellis, John; Mavromatos, Nikolaos; Nanopoulos, Dimitri; Sakharov, Alexander
2004-01-01
We present a specific model for cosmological inflation driven by the Liouville field in a non-critical supersymmetric string framework, in which the departure from criticality is due to open strings stretched between two moving Type-II 5-branes. We use WMAP and other data on fluctuations in the cosmic microwave background to fix the parameters of the model, such as the relative separation and velocity of the 5-branes, respecting also the constraints imposed by data on light propagation from distant gamma-ray bursters. The model also suggests a small, relaxing component in the present vacuum energy that may accommodate the breaking of supersymmetry
Sturm--Liouville eigenvalue problem
Bailey, P.B.
1977-01-01
The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular
A covariant canonical description of Liouville field theory
Papadopoulos, G.; Spence, B.
1993-03-01
This paper presents a new parametrisation of the space of solutions of Liouville field theory on a cylinder. In this parametrisation, the solutions are well-defined and manifestly real functions over all space-time and all of parameter space. It is shown that the resulting covariant phase space of the Liouville theory is diffeomorphic to the Hamiltonian one, and to the space of initial data of the theory. The Poisson brackets are derived and shown to be those of the co-tangent bundle of the loop group of the real line. Using Hamiltonian reduction, it is shown that this covariant phase space formulation of Liouville theory may also be obtained from the covariant phase space formulation of the Wess-Zumino-Witten model. 19 refs
Higher-spin flat space cosmologies with soft hair
Ammon, Martin [Theoretisch-Physikalisches Institut, Friedrich-Schiller University of Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Grumiller, Daniel [Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); CMCC-Universidade Federal do ABC,Santo André, S.P. (Brazil); Prohazka, Stefan [Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Riegler, Max [Université libre de Bruxelles, Boulevard du Triomphe, Campus de la Plaine,1050 Bruxelles (Belgium); Wutte, Raphaela [Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
2017-05-08
We present and discuss near horizon boundary conditions for flat space higher-spin gravity in three dimensions. As in related work our boundary conditions ensure regularity of the solutions independently of the charges. The asymptotic symmetry algebra is given by a set of û(1) current algebras. The associated charges generate higher-spin soft hair. We derive the entropy for solutions that are continuously connected to flat space cosmologies and find the same result as in the spin-2 case: the entropy is linear in the spin-2 zero-mode charges and independent from the spin-3 charges. Using twisted Sugawara-like constructions of higher-spin currents we show that our simple result for entropy of higher-spin flat space cosmologies coincides precisely with the complicated earlier results expressed in terms of higher-spin zero mode charges.
Supersymmetries and constants of motion in spinning spaces
Visinescu, Mihai
1999-01-01
The models of relativistic particles with spin have been proposed for a long time. The first published work concerning the Lagrangian description of the relativistic particle with spin was the paper by Frenkel which appeared in 1926. After that the literature on the particle with spin grew vast. The models involving only conventional coordinates are called the classical models while the models involving anticommuting (Grassmann) coordinates are generally called pseudo-classical. We shall confine ourselves to discuss the relativistic spin one half particle models involving anticommuting vectorial degrees of freedom which are usually called spinning particles. Spinning particles are in some sense the classical limit of the Dirac particles. After the first quantization these new anticommuting variables are mapped into the Dirac matrices and they disappear from the theory. We investigate the motion of pseudo-classical spinning point particles in curved spaces. The generalized Killing equations for the configuration space of spinning particles (spinning space) are analyzed and the solutions are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT spinning space. (author)
Conformal higher spin theory and twistor space actions
Hähnel, Philipp; McLoughlin, Tristan
2017-12-01
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we conjecture anti-self-dual interaction terms which give an implicit definition of a twistor action for the full conformal higher spin theory.
Minimal Liouville gravity correlation numbers from Douglas string equation
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur
2014-01-01
We continue the study of (q,p) Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of http://dx.doi.org/10.1016/0550-3213(91)90548-Chttp://dx.doi.org/10.1088/1751-8113/42/30/304004, where Lee-Yang series (2,2s+1) was studied, to (3,3s+p 0 ) Minimal Liouville Gravity, where p 0 =1,2. We demonstrate that there exist such coordinates τ m,n on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates τ m,n are related in a non-linear fashion to the natural coupling constants λ m,n of the perturbations of Minimal Lioville Gravity by the physical operators O m,n . We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature http://dx.doi.org/10.1103/PhysRevLett.66.2051http://dx.doi.org/10.1007/s11232-005-0003-3http://dx.doi.org/10.1007/s11232-006-0075-8
Spin Gauge Theory of Gravity in Clifford Space
Pavsic, Matej
2006-01-01
A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: 'extra dimensions' are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1) x SU(2) x SU(3) gauge group. The representation space for the latter group is provided by 16-component generalized spinors composed of four usual 4-component spinors, defined geometrically as the members of four independent minimal left ideals of Clifford algebra
Unitarity in three-dimensional flat space higher spin theories
Grumiller, D.; Riegler, M.; Rosseel, J.
2014-01-01
We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean W_4"("2"−"1"−"1") algebra. We extend this no-go result to rule out unitary “multi-graviton” theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.
Topological strings from Liouville gravity
Ishibashi, N.; Li, M.
1991-01-01
We study constrained SU(2) WZW models, which realize a class of two-dimensional conformal field theories. We show that they give rise to topological gravity coupled to the topological minimal models when they are coupled to Liouville gravity. (orig.)
Light-front higher-spin theories in flat space
Ponomarev, Dmitry; Skvortsov, Evgeny
2017-03-01
We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.
Light-front higher-spin theories in flat space
Ponomarev, Dmitry; Skvortsov, Evgeny
2017-01-01
We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local. (paper)
Bosonic Liouville string theory in conformal gauge
Schnittger, J.
1990-01-01
The object of the present thesis are the so-called Liouville theories as possibilities for the consistent formulation of string theories beyond the critical dimension. First we discuss the general framework for the quantum theory and explain common properties and differences of different approaches. These considerations lead us to the main demand of the thesis, the formulation of a unified quantum theory for open and closed strings. Of central importance is thereby the construction of the field operator for the Weyl degree of freedom on a suitably defined Hilbert space, so that also in the quantum theory locality and Hermiticity of the Energy-Momentum tensor are respected. In the study of the allowed ground states of the Hilbert space an interesting particularity in comparison to the structure of usual conformal field theories comes across, the importance and consequences of which we intensively study. In the last section we enter the consistence of the theory on the 1-loop level and come then to the final consideration, where we indicate some still open questions of the Liouville theory. (orig.) [de
A quantum group approach to cL > 1 Liouville gravity
Suzuki, Takashi.
1995-03-01
A candidate of c L > 1 Liouville gravity is studied via infinite dimensional representations of U q sl(2, C) with q at a root of unity. We show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from finite dimensional representations of U q sl(2, C). Expressions of correlation functions and transition amplitudes are presented. We discuss about our results and find an intimate relation between our quantization of the Liouville theory and the geometric quantization of moduli space of Riemann surfaces. An interpretation of quantum space-time is also given within this formulation. (author)
Hardy inequality and properties of the quasilinear Sturm-Liouville problem
Drábek, P.; Kufner, Alois
2007-01-01
Roč. 18, č. 1 (2007), s. 125-138 ISSN 1120-6330 Institutional research plan: CEZ:AV0Z10190503 Keywords : Hardy inequality * weighted spaces * Sturm-Liouville problem Subject RIV: BA - General Mathematics
Magnetic De-spinning of Space Objects
National Aeronautics and Space Administration — Objects in orbit about the earth rotate such that a service spacecraft cannot grapple to them. There are few techniques available to despin a space object without...
Higher spin currents in Wolf space. Part I
Ahn, Changhyun [Department of Physics, Kyungpook National University,Taegu 702-701 (Korea, Republic of)
2014-03-20
For the N=4 superconformal coset theory described by ((SU(N+2))/(SU(N))) (that contains a Wolf space) with N=3, the N=2 WZW affine current algebra with constraints is obtained. The 16 generators of the large N=4 linear superconformal algebra are described by those WZW affine currents explicitly. By factoring out four spin-(1/2) currents and the spin-1 current from these 16 generators, the remaining 11 generators (spin-2 current, four spin-(3/2) currents, and six spin-1 currents) corresponding to the large N=4 nonlinear superconformal algebra are obtained. Based on the recent work by Gaberdiel and Gopakumar on the large N=4 holography, the extra 16 currents, with spin contents (1,(3/2),(3/2),2), ((3/2),2,2,(5/2)), ((3/2),2,2,(5/2)), and (2,(5/2),(5/2),3) described in terms of N=2 multiplets, are obtained and realized by the WZW affine currents. As a first step towards N=4W algebra (which is NOT known so far), the operator product expansions (OPEs) between the above 11 currents and these extra 16 higher spin currents are found explicitly. It turns out that the composite fields with definite U(1) charges, made of above (11+16) currents (which commute with the Wolf space subgroup SU(N=3)×SU(2)×U(1) currents), occur in the right hand sides of these OPEs.
Liouville gravity on bordered surfaces
Jaskolski, Z.
1991-11-01
The functional quantization of the Liouville gravity on bordered surfaces in the conformal gauge is developed. It was shown that the geometrical interpretation of the Polyakov path integral as a sum over bordered surfaces uniquely determines the boundary conditions for the fields involved. The gravitational scaling dimensions of boundary and bulk operators and the critical exponents are derived. In particular, the boundary Hausdorff dimension is calculated. (author). 21 refs
Conformal higher spin scattering amplitudes from twistor space
Adamo, Tim [Blackett Laboratory, Imperial College, London, SW7 2AZ (United Kingdom); Hähnel, Philipp; McLoughlin, Tristan [School of Mathematics, Trinity College Dublin, College Green, Dublin 2 (Ireland)
2017-04-04
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
Conformal higher spin scattering amplitudes from twistor space
Adamo, Tim; Hähnel, Philipp; McLoughlin, Tristan
2017-01-01
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
The many faces of the quantum Liouville exponentials
Gervais, Jean-Loup; Schnittger, Jens
1994-01-01
First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.
Higher-spin algebras, holography and flat space
Sleight, C. [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805 Munich (Germany); Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium); Taronna, M. [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium)
2017-02-20
In this article we study the higher-spin algebra behind the type-A cubic couplings recently extracted from the free O(N) model in generic dimensions, demonstrating that they coincide with the known structure constants for the unique higher-spin algebra in generic dimensions. This provides an explicit check of the holographic reconstruction and of the duality between higher-spin theories and the free O(N) model in generic dimensions, generalising the result of Giombi and Yin in AdS{sub 4}. For completeness, we also address the same problem in the flat space for the cubic couplings derived by Metsaev in 1991, which are recovered from the flat limit of the AdS type-A cubic couplings. We observe that both flat and AdS{sub 4} higher-spin Lorentz subalgebras coincide, hinting towards the existence of a full higher-spin symmetry behind the flat-space cubic couplings of Metsaev.
Gauge theory loop operators and Liouville theory
Drukker, Nadav; Teschner, Joerg
2009-10-01
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S 4 - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
Exact solution of super Liouville model
Yang Zhanying; Zhao Liu; Zhen Yi
2000-01-01
Using Leznov-Saveliev algebraic analysis and Drinfeld-Sokolov construction, the authors obtained the explicit solutions to the super Liouville system in super covariant form and component form. The explicit solution in component form reduces naturally into the Egnchi-Hanson instanton solution of the usual Liouville equation if all the Grassmann odd components are set equal to zero
Gauge theory loop operators and Liouville theory
Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2009-10-15
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
Covariant currents in N=2 super-Liouville theory
Gomis, J.; Suzuki, Hiroshi
1993-01-01
Based on a path-integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N=2 supergravity, i.e. N=2 super-Liouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost-number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost-number supercurrents in the effective theory. We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is in great contrast with N=0 and N=1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions. Our observation suggests a topological nature of the two-dimensional N=2 supergravity as a quantum theory. (orig.)
H3+-WZNW correlators from Liouville theory
Ribault, Sylvain; Teschner, Joerg
2005-01-01
We prove that arbitrary correlation functions of the H 3 + -WZNW model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H 3 + -WZNW model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) gauged WZNW model in terms of correlation functions in Liouville theory
Zimmerman, Paul M; Bell, Franziska; Goldey, Matthew; Bell, Alexis T; Head-Gordon, Martin
2012-10-28
The restricted active space spin flip (RAS-SF) method is extended to allow ground and excited states of molecular radicals to be described at low cost (for small numbers of spin flips). RAS-SF allows for any number of spin flips and a flexible active space while maintaining pure spin eigenfunctions for all states by maintaining a spin complete set of determinants and using spin-restricted orbitals. The implementation supports both even and odd numbers of electrons, while use of resolution of the identity integrals and a shared memory parallel implementation allow for fast computation. Examples of multiple-bond dissociation, excited states in triradicals, spin conversions in organic multi-radicals, and mixed-valence metal coordination complexes demonstrate the broad usefulness of RAS-SF.
Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Suchanek, Paulina [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Univ. of Wroclaw (Poland). Inst. for Theoretical Physics
2012-10-15
N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1 vertical stroke 2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is standard, the second turns out to be imaginary (or time-like). We extend the proposal to the R sector and perform extensive checks based on detailed comparison of 3-point functions involving several super-conformal primaries and descendants. On the basis of such strong evidence we sketch a number of interesting potential applications of this intriguing bozonization.
Semiclassical limit of the FZZT Liouville theory
Hadasz, Leszek; Jaskolski, Zbigniew
2006-01-01
The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators
Semiclassical limit of the FZZT Liouville theory
Hadasz, Leszek; Jaskólski, Zbigniew
2006-11-01
The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.
Semiclassical limit of the FZZT Liouville theory
Hadasz, Leszek; Jaskolski, Zbigniew
2006-01-01
The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: one bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.
Semiclassical limit of the FZZT Liouville theory
Hadasz, Leszek [Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universitaet, Nussallee 12, 53115 Bonn (Germany); M. Smoluchowski Institute of Physics, Jagiellonian University, W. Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204 Wroclaw (Poland)]. E-mail: jask@ift.uni.wroc.pl
2006-11-27
The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: One bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.
Liouville equation of relativistic charged fermion
Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming
1991-01-01
As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function
A quantum group approach to c{sub L} > 1 Liouville gravity
Suzuki, Takashi
1995-03-01
A candidate of c{sub L} > 1 Liouville gravity is studied via infinite dimensional representations of U{sub q}sl(2, C) with q at a root of unity. We show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from finite dimensional representations of U{sub q}sl(2, C). Expressions of correlation functions and transition amplitudes are presented. We discuss about our results and find an intimate relation between our quantization of the Liouville theory and the geometric quantization of moduli space of Riemann surfaces. An interpretation of quantum space-time is also given within this formulation. (author).
Touching random surfaces and Liouville gravity
Klebanov, I.R.
1995-01-01
Large N matrix models modified by terms of the form g(TrΦ n ) 2 generate random surfaces which touch at isolated points. Matrix model results indicate that, as g is increased to a special value g t , the string susceptibility exponent suddenly jumps from its conventional value γ to γ/(γ-1). We study this effect in Liouville gravity and attribute it to a change of the interaction term from Oe α + φ for g t to Oe α - φ for g=g t (α + and α - are the two roots of the conformal invariance condition for the Liouville dressing of a matter operator O). Thus, the new critical behavior is explained by the unconventional branch of Liouville dressing in the action
Sturm-Liouville operators and applications
Marchenko, Vladimir A
2011-01-01
The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl
2004-08-30
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek; Jaskólski, Zbigniew
2004-08-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek; Jaskolski, Zbigniew
2004-01-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory
Martens, Craig C., E-mail: cmartens@uci.edu
2016-12-20
In this paper, we revisit the semiclassical Liouville approach to describing molecular dynamics with electronic transitions using classical trajectories. Key features of the formalism are highlighted. The locality in phase space and presence of nonclassical terms in the generalized Liouville equations are emphasized and discussed in light of trajectory surface hopping methodology. The representation dependence of the coupled semiclassical Liouville equations in the diabatic and adiabatic bases are discussed and new results for the transformation theory of the Wigner functions representing the corresponding density matrix elements given. We show that the diagonal energies of the state populations are not conserved during electronic transitions, as energy is stored in the electronic coherence. We discuss the implications of this observation for the validity of imposing strict energy conservation in trajectory based methods for simulating nonadiabatic processes.
Modular bootstrap in Liouville field theory
Hadasz, Leszek; Jaskolski, Zbigniew; Suchanek, Paulina
2010-01-01
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Modular bootstrap in Liouville field theory
Hadasz, Leszek, E-mail: hadasz@th.if.uj.edu.p [M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland); Jaskolski, Zbigniew, E-mail: jask@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland); Suchanek, Paulina, E-mail: paulina@ift.uni.wroc.p [Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna, 50-204 Wroclaw (Poland)
2010-02-22
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Modular bootstrap in Liouville field theory
Hadasz, Leszek; Jaskólski, Zbigniew; Suchanek, Paulina
2010-02-01
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
'Footballs', conical singularities, and the Liouville equation
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Sturm-Liouville BVPs with Caratheodory nonlinearities
Abdelhamid Benmezai
2016-11-01
Full Text Available In this article we study the existence and multiplicity of solutions for several classes of Sturm-Liouville boundary value problems having Caratheodory nonlinearities. Many results existing in the literature for such boundary value problems in the continuous framework will find in this work their extensions to the Caratheodory setting.
Supersymmetries and constants of motion in Taub-NUT spinning space
Vaman, D.; Visinescu, M.
1998-01-01
Models of relativistic particles with spin have been proposed for a long time. The models involving only conventional coordinates are called classical, while the models involving anticommuting coordinates are generally called pseudo-classical. In this paper, the relativistic spin one half particle models involving anticommuting vectorial degrees of freedom, which are usually called the spinning particles, are considered. Spinning particles are in some sense the classical limit of the Dirac particles. After the first quantization these new anticommuting variables are mapped into the Dirac matrices and they disappear from the theory. In the present paper, the motion of pseudo-classical spinning particles in curved spaces is investigated and the relevant equations of motion are investigated. The generalized Killing equations for the configuration space of spinning particles (spinning spaces) are discussed and the constants of motion are derived in terms of the solutions of these equations. We also analysed the motion of pseudo-classical spinning particles in the Euclidean Taub-NUT space. The generalized Killing equations for this spinning space are examined and derivation of the constants of motion in terms of the Killing-Yano tensors is described. The equations obtained for the special case of motion on cone are solved. This case represents an extension of the scalar particle motions in the usual Taub-NUT space in which the orbits are conic sections. An explicit exact solution is given. In spite of its simplicity, this solution occurs to be far from trivial. (authors)
Classical geometry from the quantum Liouville theory
Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin
2005-09-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl
2005-09-26
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin
2005-01-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere
Unitarity relations in c=1 Liouville theory
Lowe, D.A.
1992-01-01
In this paper, the authors consider the S-matrix of c = 1 Liouville theory with vanishing cosmological constant. The authors examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the plus tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, the authors show that the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. The authors conclude with some comments about the genus one (N,2) amplitudes
Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space
Vasiliev, M A
1988-04-25
Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.
A Note on Upper Tail Behavior of Liouville Copulas
Lei Hua
2016-11-01
Full Text Available The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail behavior of Liouville copulas through their upper tail orders. Tail orders of a more general scale mixture model that covers Liouville distributions is first derived, and then tail order functions and tail order density functions of Liouville copulas are derived. Concrete examples are given after the main results.
Particle spin dynamics as the grassmann variant of classical mechanics
Berezin, F.A.; Marinov, M.S.
1976-01-01
A generalization of the calssical mechanics is presented. The dynamical variables are assumed to be elements of an algebra with anticommuting generators (The Grassmann algebra). The action functional and the Poisson brackets are defined. The equations of motion are deduced from the variational principle. The dynamics is described also by means of the Liouville equation for the phase-space distribution. The canonical quantization lead phase-space path integral approach to the quantum theory is also formulated. The theory is applied to describe the particle spin. Classical description of the spin precession and of the spin-orbital forces is given. The phase-space distribution and the interaction with an external field are also considered
Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis
Hadasz, Leszek; Jaskólski, Zbigniew
The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.
Rotational bands terminating at maximal spin in the valence space
Ragnarsson, I.; Afanasjev, A.V. [Lund Institute of Technology (Sweden)
1996-12-31
For nuclei with mass A {le} 120, the spin available in {open_quotes}normal deformation configurations{close_quotes} is experimentally accessible with present detector systems. Of special interest are the nuclei which show collective features at low or medium-high spin and where the corresponding rotational bands with increasing spin can be followed in a continuous way to or close to a non-collective terminating state. Some specific features in this context are discussed for nuclei in the A = 80 region and for {sup 117,118}Xe.
Liouville theory with a central charge less than one
Ribault, Sylvain [CEA Saclay, Institut de Physique Théorique,F-91191, Gif-sur-Yvette (France); Santachiara, Raoul [LPTMS, Université Paris Sud,15 rue Georges Clemenceau, Orsay (France)
2015-08-21
We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always spacelike, and there is no consistent timelike Liouville theory. We also study the non-analytic conformal field theories that exist at rational values of the central charge. Our claims are supported by numerical checks of crossing symmetry. We provide Python code for computing Virasoro conformal blocks, and correlation functions in Liouville theory and (generalized) minimal models.
The Sturm-Liouville spectrum problem: quartic oscillator case
Voros, Andre.
1982-11-01
The Sturm-Liouville eigenvalue problem given by the steady-state Schroedinger equation in quantum mechanics is considered on the real axis. There are, however, exact expressions available only for a harmonic oscillator (the Hermite equation); consequently, semi-classical asymptotic methods (in powers of the Planck's constant), which yield very good approximations, have been much studied analytically and as regards their relationships to geometrical optics. These methods relate the asymptotic form of the spectrum to the closed orbits of the Hamiltonian vector field of the function H(p,q) = p 2 + V(q) in the phase space R 2 . We seek to show that these supposedly approximate methods are in fact an exact way of solving the problem. The quartic oscillator, with V(q) = q 4 , is used as an example [fr
The Picard group of the moduli space of r-Spin Riemann surfaces
Randal-Williams, Oscar
2012-01-01
An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford...... conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles....
On the Fock space realizations of nonlinear algebras describing the high spin fields in AdS spaces
Burdik, C.; Navratil, O.; Pashnev, A.
2002-01-01
The method of construction of Fock space realizations of Lie algebras is generalized for nonlinear algebras. We consider as an example the nonlinear algebra of constraints which describe the totally symmetric fields with higher spins in the AdS space-time
On Multi-Point Liouville Field Theory
Zarrinkamar, S.; Rajabi, A. A.; Hassanabadi, H.
2013-01-01
In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or at least require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field. (author)
Dressing symmetry of the uniformization solution of Liouville equation
Shen Jianmin.
1994-10-01
In this paper, the relations between monodromy group and dressing group for Liouville equation in uniformization theorem are discussed. The representation of monodromy transformation, acting on the chiral components of the solution of Liouville equation, is obtained. The non-trivial exchange algebra for monodromy transformation is calculated. (author). 14 refs
Phase-space spinor amplitudes for spin-1/2 systems
Watson, P.; Bracken, A. J.
2011-01-01
The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-(1/2) is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-(1/2) magnetic dipole in a time-dependent magnetic field.
Phase-space curvature in spin-orbit-coupled ultracold atomic systems
Armaitis, J.; Ruseckas, J.; Anisimovas, E.
2017-04-01
We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles with equal Rashba-Dresselhaus spin-orbit coupling in one dimension. In our derivation, the adiabatic transformation is performed first and leads to quantum Heisenberg equations of motion for momentum and position operators. These equations explicitly contain position-space, momentum-space, and phase-space Berry curvature terms. Subsequently, we perform the semiclassical approximation and obtain the semiclassical equations of motion. Taking the low-Berry-curvature limit results in equations that can be directly compared to previous results for the motion of wave packets. Finally, we show that in the semiclassical regime, the effective mass of the equal Rashba-Dresselhaus spin-orbit-coupled system can be viewed as a direct effect of the phase-space Berry curvature.
Diamond Electron-Spin Clocks For Space Navigation and Communication
National Aeronautics and Space Administration — Precision clocks are needed in a broad range of applications, including satellite communication, high-bandwidth wireless communication, computing systems, and...
Separation of massive field equation of arbitrary spin in Robertson-Walker space-time
Zecca, A.
2006-01-01
The massive spin-(3/2) field equation is explicitly integrated in the Robertson-Walker space-time by the Newman Penrose formalism. The solution is obtained by extending a separation procedure previously used to solve the spin-1 equation. The separated time dependence results in two coupled equations depending on the cosmological background evolution. The separated angular equations are explicitly integrated and the eigenvalues determined. The separated radial equations are integrated in the flat space-time case. The separation method of solution is then generalized, by induction, to prove the main result, that is the separability of the massive field equations of arbitrary spin in the Robertson-Walker space-time
The Solution Construction of Heterotic Super-Liouville Model
Yang, Zhan-Ying; Zhen, Yi
2001-12-01
We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld-Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liouville model, we obtain the conserved current and conserved charge which possessed the BRST properties.
Two- and three-point functions in Liouville theory
Dorn, H.; Otto, H.J.
1994-04-01
Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself. (orig.)
Real-space imaging of non-collinear antiferromagnetic order with a single-spin magnetometer
Gross, I.; Akhtar, W.; Garcia, V.; Martínez, L. J.; Chouaieb, S.; Garcia, K.; Carrétéro, C.; Barthélémy, A.; Appel, P.; Maletinsky, P.; Kim, J.-V.; Chauleau, J. Y.; Jaouen, N.; Viret, M.; Bibes, M.; Fusil, S.; Jacques, V.
2017-09-01
Although ferromagnets have many applications, their large magnetization and the resulting energy cost for switching magnetic moments bring into question their suitability for reliable low-power spintronic devices. Non-collinear antiferromagnetic systems do not suffer from this problem, and often have extra functionalities: non-collinear spin order may break space-inversion symmetry and thus allow electric-field control of magnetism, or may produce emergent spin-orbit effects that enable efficient spin-charge interconversion. To harness these traits for next-generation spintronics, the nanoscale control and imaging capabilities that are now routine for ferromagnets must be developed for antiferromagnetic systems. Here, using a non-invasive, scanning single-spin magnetometer based on a nitrogen-vacancy defect in diamond, we demonstrate real-space visualization of non-collinear antiferromagnetic order in a magnetic thin film at room temperature. We image the spin cycloid of a multiferroic bismuth ferrite (BiFeO3) thin film and extract a period of about 70 nanometres, consistent with values determined by macroscopic diffraction. In addition, we take advantage of the magnetoelectric coupling present in BiFeO3 to manipulate the cycloid propagation direction by an electric field. Besides highlighting the potential of nitrogen-vacancy magnetometry for imaging complex antiferromagnetic orders at the nanoscale, these results demonstrate how BiFeO3 can be used in the design of reconfigurable nanoscale spin textures.
Phase-space lagrangians for null spinning strings
Barcelos-Neto, J.; Ruiz-Altaba, M.; Ramirez, C.
1990-01-01
The striking fact that normal-ordered null strings have the same critical dimension as their usual non-zero tension siblings can be understood from the observation that one must, in the tensionless case, keep all the conjugate momenta as independent dynamical variables, thus doubling the number of physical degrees of freedom. The fermionic momenta give rise to a second-class constraint which cannot be solved covariantly, but can be successfully incorporated into the first-class constraint algebra after gauge-fixing. The ghost contributions to the anomaly consist of two b-c (and also two β-γ systems in the supersymmetric case), of the single Virasoro sub(super)algebra for the closed null (spinning) string. In the appropriate gauge, the null (super)string is (super)chiral. (orig.)
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti; Rundell, William
2012-01-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical
The exchange algebra for Liouville theory on punctured Riemann sphere
Shen Jianmin; Sheng Zhengmao
1991-11-01
We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs
Liouville theory and uniformization of four-punctured sphere
Hadasz, Leszek; Jaskolski, Zbigniew
2006-01-01
Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four ...
Defects and permutation branes in the Liouville field theory
Sarkissian, Gor
2009-01-01
The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families.......The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of solutions exist, discrete and continuous families....
Green's functions for spin half field theory in Rindler space
Iyer, B.R.; Kumar, Arvind
1977-01-01
The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green's functions are written down in the two casually disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green's functions in all regions is exhibited. (author)
Green's functions for spin half field theory in Rindler space
Iyer, B R; Kumar, Arvind [Birla Inst. of Tech., Ranchi (India). Dept. of Physics
1977-11-01
The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green's functions are written down in the two casually disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green's functions in all regions is exhibited.
Distance measurement and wave dispersion in a Liouville-string approach to quantum gravity
Amelino-Camelia, G; Mavromatos, Nikolaos E; Nanopoulos, Dimitri V
1997-01-01
Within a Liouville approach to non-critical string theory, we discuss space-time foam effects on the propagation of low-energy particles. We find an induced frequency-dependent dispersion in the propagation of a wave packet, and observe that this would affect the outcome of measurements involving low-energy particles as probes. In particular, the maximum possible order of magnitude of the space-time foam effects would give rise to an error in the measurement of distance comparable to that independently obtained in some recent heuristic quantum-gravity analyses. We also briefly compare these error estimates with the precision of astrophysical measurements.
The motion of a classical spinning point particle in a Riemann-Cartan space-time
Amorim, R.
1983-01-01
A consistent set of equations of motion for classical charged point particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a generalized Lagrangean formalism. The equations avoid the spurius free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are paralell in this theory, where the condition of orthogonality between the spin and the 4-velocity is treated as a non-holonomic one. (Author) [pt
Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space
Buchbinder, I.L.; Snegirev, T.V.; Zinoviev, Yu.M.
2012-01-01
We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional (A)dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
Nonequilibrium dynamics of spin-boson models from phase-space methods
Piñeiro Orioli, Asier; Safavi-Naini, Arghavan; Wall, Michael L.; Rey, Ana Maria
2017-09-01
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase-space methods such as the truncated Wigner approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [J. Schachenmayer, A. Pikovski, and A. M. Rey, Phys. Rev. X 5, 011022 (2015), 10.1103/PhysRevX.5.011022]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations to our coupled spin-boson model. This allows us, in principle, to study how systematically adding higher-order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model, which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for an arbitrary number of bosonic modes.
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
Ding You; Rovelli, Carlo
2010-01-01
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit). We also generalize the definition of the volume operator in the spin-foam model to the Lorentzian signature and show that it matches the one of loop quantum gravity, as in the Euclidean case.
Berry phase for spin-1/2 particles moving in a space-time with torsion
Alimohammadi, M.; Shariati, A.
2001-01-01
Berry phase for a spin-1/2 particle moving in a flat space-time with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks. (orig.)
Berry phase for spin-1/2 particles moving in a space-time with torsion
Alimohammadi, M. [Dept. of Physics, Tehran Univ. (Iran); Shariati, A. [Inst. for Advanced Studies in Basic Sciences, Zanjan (Iran); Inst. for Studies in Theoretical Physics and Mathematics, Tehran (Iran)
2001-06-01
Berry phase for a spin-1/2 particle moving in a flat space-time with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks. (orig.)
SD-CAS: Spin Dynamics by Computer Algebra System.
Filip, Xenia; Filip, Claudiu
2010-11-01
A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples. Copyright © 2010 Elsevier Inc. All rights reserved.
Inequalities among eigenvalues of Sturm–Liouville problems
Kong Q
1999-01-01
Full Text Available There are well-known inequalities among the eigenvalues of Sturm–Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm–Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm–Liouville problems without using operator theory.
Dynamics and constraints of the Dissipative Liouville Cosmology
Basilakos, Spyros; Mitsou, Vasiliki A; Plionis, Manolis
2012-01-01
In this article we investigate the properties of the FLRW flat cosmological models in which the cosmic expansion of the Universe is affected by a dilaton dark energy (Liouville scenario). In particular, we perform a detailed study of these models in the light of the latest cosmological data, which serves to illustrate the phenomenological viability of the new dark energy paradigm as a serious alternative to the traditional scalar field approaches. By performing a joint likelihood analysis of the recent supernovae type Ia data (SNIa), the differential ages of passively evolving galaxies, and the Baryonic Acoustic Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS), we put tight constraints on the main cosmological parameters. Furthermore, we study the linear matter fluctuation field of the above Liouville cosmological models. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current Liouville models. Performing vari...
H+3 WZNW model from Liouville field theory
Hikida, Yasuaki; Schomerus, Volker
2007-01-01
There exists an intriguing relation between genus zero correlation functions in the H + 3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program
Similarities of discrete and continuous Sturm-Liouville problems
Kazem Ghanbari
2007-12-01
Full Text Available In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green's functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl's m-function determines the Sturm-Liouville operators uniquely. Moreover, the well known Rayleigh-Ritz Theorem in linear algebra can be proved by using the concept of Green's function in discrete case.
Liouville theory and uniformization of four-punctured sphere
Hadasz, Leszek; Jaskólski, Zbigniew
2006-08-01
A few years ago Zamolodchikov and Zamolodchikov proposed an expression for the four-point classical Liouville action in terms of the three-point actions and the classical conformal block [Nucl. Phys. B 477, 577 (1996)]. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.
The local structure of a Liouville vector field
Ciriza, E.
1990-05-01
In this work we investigate the local structure of a Liouville vector field ξ of a Kaehler manifold (P,Ω) which vanishes on an isotropic submanifold Q of P. Some of the eigenvalues of its linear part at the singular points are zero and the remaining ones are in resonance. We show that there is a C 1 -smooth linearizing conjugation between the Liouville vector field ξ and its linear part. To do this we construct Darboux coordinates adapted to the unstable foliation which is provided by the Centre Manifold Theorem. We then apply recent linearization results due to G. Sell. (author). 11 refs
Theory of a higher-order Sturm-Liouville equation
Kozlov, Vladimir
1997-01-01
This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.
The Interaction of Physics, Mechanics and Mathematics in Joseph Liouville's Research
Lützen, Jesper
2013-01-01
Som for mange af hans samtidige var fysik og mekanik en stor inspirationskilde for Liouville's matematiske forskning. Laplaces tilgang til fysik var oprindelsen til Liouvilles teori om differentiation af vilkårlig orden, Kelvins elektrostatiske forskning var oprindelsen til Liouvilles sætning om ...
Hassanabadi, Hassan; Zare, Soroush; Sobhani, Hadi [Shahrood University of Technology, Faculty of Physics, Shahrood (Iran, Islamic Republic of); Chung, Won Sang [Gyeongsang National University, Department of Physics and Research Institute of Natural Science, College of Natural Science, Jinju (Korea, Republic of)
2018-01-15
This paper contains a discussion of a relativistic spin-0 system in the presence of a Goedel-type background space-time. The Duffin-Kemmer-Petiau (DKP) equation in the presence of a Goedel-type background space-time is studied in detail. After a derivation of the final form of this equation in the considered framework, free spin-0 particles have been studied. (orig.)
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
J. Schachenmayer
2015-02-01
Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
On the non-local obstruction to interacting higher spins in flat space
Taronna, Massimo [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium)
2017-05-04
Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic couplings with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of 1/◻ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities in the general quartic Noether procedure solution with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in d=4, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.
Quantization of bosonic closed strings and the Liouville model
Paycha, S.
1988-01-01
The author shows that by means of a reasonable interpretation of the Lebesgue measure describing the partition function the quantization of closed bosonic strings described by compact surfaces of genus p>1 can be related to that of the Liouville model. (HSI)
Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition
Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)
2014-12-15
In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.
Selfadjointness of the Liouville operator for infinite classical systems
Marchioro, C [Camerino Univ. (Italy). Istituto di Matematica; Pellegrinotti, A [Rome Univ. (Italy). Istituto di Matematica; Pulvirenti, M [Ancona Univ. (Italy). Istituto di Matematica
1978-02-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed.
An efficient method for solving fractional Sturm-Liouville problems
Al-Mdallal, Qasem M.
2009-01-01
The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.
Liouville's theorem and the method of the inverse problem
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
On the solution of the Liouville equation over a rectangle
A. M. Arthurs
1996-01-01
Full Text Available Methods for integral equations are used to derive pointwise bounds for the solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the resulting solutions are more accurate than those obtained previously by other methods.
Selfadjointness of the Liouville operator for infinite classical systems
Marchioro, C.; Pellegrinotti, A.; Pulvirenti, M.
1978-01-01
We study some properties of the time evolution of an infinite one dimensional hard core system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint an the algebra of local observables. Some consequences of this result are also discussed. (orig.) [de
Weyl transforms associated with the Riemann-Liouville operator
N. B. Hamadi
2006-01-01
Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.
Liouville equation with boundary conditions derived from classical strings
Marnelius, R.
1983-01-01
It is shown in terms of the classical string theory that a breaking of the Weyl invariance necessarily requires the Liouville equation for the variable phi=1n rho, where rho is the variable that appears in the conformal gauge gsub(α#betta#)=rhoetasub(α#betta#). Appropriate boundary conditions on phi for open and closed strings are then derived. (orig.)
Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes
Lim, S C; Teo, L P
2007-01-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established
Calzetta, E.; Habib, S.; Hu, B.L.
1988-01-01
We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe
P.-N. Seo
2008-08-01
Full Text Available High precision fundamental neutron physics experiments have been proposed for the intense pulsed spallation neutron beams at JSNS, LANSCE, and SNS to test the standard model and search for new physics. Certain systematic effects in some of these experiments have to be controlled at the few ppb level. The NPDGamma experiment, a search for the small parity-violating γ-ray asymmetry A_{γ} in polarized cold neutron capture on parahydrogen, is one example. For the NPDGamma experiment we developed a radio-frequency resonant spin rotator to reverse the neutron polarization in a 9.5 cm×9.5 cm pulsed cold neutron beam with high efficiency over a broad cold neutron energy range. The effect of the spin reversal by the rotator on the neutron beam phase space is compared qualitatively to rf neutron spin flippers based on adiabatic fast passage. We discuss the design of the spin rotator and describe two types of transmission-based neutron spin-flip efficiency measurements where the neutron beam was both polarized and analyzed by optically polarized ^{3}He neutron spin filters. The efficiency of the spin rotator was measured at LANSCE to be 98.8±0.5% for neutron energies from 3 to 20 meV over the full phase space of the beam. Systematic effects that the rf spin rotator introduces to the NPDGamma experiment are considered.
Monthus, Cécile
2017-07-01
When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.
Virtual walks in spin space: A study in a family of two-parameter models
Mullick, Pratik; Sen, Parongama
2018-05-01
We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys. A 26, 2317 (1993), 10.1088/0305-4470/26/10/006]. The behavior of S (x ,t ) , the probability that the walker is at position x at time t , is studied in detail. In general S (x ,t ) ˜t-αf (x /tα) with α ≃1 or 0.5 at large times depending on the parameters. In particular, S (x ,t ) for the point y =1 ,z =0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L2logL . We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S (x ,t ) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.
Effect of spin-polarized D-3He fuel on dense plasma focus for space propulsion
Mei-Yu Wang, Choi, Chan K.; Mead, Franklin B.
1992-01-01
Spin-polarized D-3He fusion fuel is analyzed to study its effect on the dense plasma focus (DPF) device for space propulsion. The Mather-type plasma focus device is adopted because of the ``axial'' acceleration of the current carrying plasma sheath, like a coaxial plasma gun. The D-3He fuel is chosen based on the neutron-lean fusion reactions with high charged-particle fusion products. Impulsive mode of operation is used with multi-thrusters in order to make higher thrust (F)-to-weight (W) ratio with relatively high value of specific impulse (Isp). Both current (I) scalings with I2 and I8/3 are considered for plasma pinch temperature and capacitor mass. For a 30-day Mars mission, with four thrusters, for example, the typical F/W values ranging from 0.5-0.6 to 0.1-0.2 for I2 and I8/3 scalings, respectively, and the Isp values of above 1600 s are obtained. Parametric studies indicate that the spin-polarized D-3He provides increased values of F/W and Isp over conventional D-3He fuel which was due to the increased fusion power and decreased radiation losses for the spin-polarized case.
Chang, Zhiwei; Halle, Bertil
2016-02-28
In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.
Vasiliev, M A
1987-11-01
Linearized curvatures are constructed for massless higher spin fields on the (anti-) de Sitter background. The quite uniform description for free massless fields of all integer and half-integer spins s greater than or equal to 3/2 is presented, based on these curvatures. In particular, the actions and the equations of motion are given in a simple form. The proposed linearized curvatures provide 'initial data' for determination of a non-Abelian higher spin symmetry that may correspond to a hypothetical non-trivial theory of higher spins interacting with gravity and themselves. It is noted that the conjugation law for fermion fields should be modified drastically after transition from the anti-de-Sitter geometry to the de Sitter one.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-01-01
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
H+3 WZNW model from Liouville field theory
Hikida, Y.; Schomerus, V.
2007-06-01
There exists an intriguing relation between genus zero correlation functions in the H + 3 WZNW model and in Liouville field theory. This was found by Ribault and Teschner based in part on earlier ideas by Stoyanovsky. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program. (orig.)
Extended Riemann-Liouville type fractional derivative operator with applications
Agarwal P.
2017-12-01
Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
A hierarchy of Liouville integrable discrete Hamiltonian equations
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
Adomian decomposition method for nonlinear Sturm-Liouville problems
Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti
2012-05-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
Liouville's equation and radiative acceleration in general relativity
Keane, A.J.
1999-01-01
This thesis examines thoroughly the general motion of a material charged particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. Such a test particle will be pulled in by the gravitational attraction of the compact object and pushed out by the radiation pressure force, therefore the types of trajectory admitted will depend the gravitational field, the radiation field and the particle cross-section. The presence of a strong gravitational field demands a fully general relativistic treatment of the problem. This type of calculation is interesting not only as a formal problem in general relativity but also since it has important astrophysical implications, for example, application to astrophysical discs and jets. In chapter 1 we review the classical radiation force problem and outline the transition to a fully general relativistic scenario. We discuss the method for obtaining the radiation pressure force and calculating the particle trajectories. We review previous work in this area and outline the aims of the thesis. Then we consider some astrophysical applications and discuss how realistic our calculations are. In chapter 2 we give an introduction and overview of differential geometry as this is necessary for an accurate description of tensors on a curved manifold. Then we review the general theory of relativity and in particular obtain the Schwarzschild metric describing a static spherically symmetric vacuum spacetime. Chapter 3 deals with test particle motion through a curved spacetime. Liouville's equation describes the statistical distribution in phase space of a collection of test particles and is based upon a Hamiltonian formulation of the dynamical system - this material also relies heavily upon the concepts of differential geometry introduced in chapter 2. In particular we are interested in photon transport and find the general solutions for some symmetric
Geometric properties of static Einstein-Maxwell dilaton horizons with a Liouville potential
Abdolrahimi, Shohreh; Shoom, Andrey A.
2011-01-01
We study nondegenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d≥4) static space-times. Using Israel's description of a static space-time, we construct the EMdL equations and the space-time curvature invariants: the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that space-time metric functions and the model fields are real analytic functions in the vicinity of a space-time horizon, we study the behavior of the space-time metric and the fields near the horizon and derive relations between the space-time curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize similar relations known for horizons of static four- and five-dimensional vacuum and four-dimensional electrovacuum space-times. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present the necessary conditions for the existence of static extremal horizons within the EMdL model.
Reconstructing 1/2 BPS space-time metrics from matrix models and spin chains
Vazquez, Samuel E.
2007-01-01
Using the anti-de Sitter/conformal field theories (AdS/CFT) correspondence, we address the question of how to measure complicated space-time metrics using gauge theory probes. In particular, we consider the case of the 1/2 Bogomol'nyi-Prasad-Sommerfield geometries of type IIB supergravity. These geometries are classified by certain droplets in a two-dimensional spacelike hypersurface. We show how to reconstruct the full metric inside these droplets using the one-loop N=4 super Yang-Mills theory dilatation operator. This is done by considering long operators in the SU(2) sector, which are dual to fast rotating strings on the droplets. We develop new powerful techniques for large N complex matrix models that allow us to construct the Hamiltonian for these strings. We find that the Hamiltonian can be mapped to a dynamical spin chain. That is, the length of the chain is not fixed. Moreover, all of these spin chains can be explicitly constructed using an interesting algebra which is derived from the matrix model. Our techniques work for general droplet configurations. As an example, we study a single elliptical droplet and the hypotrochoid
Kirkpatrick, Andrew W.; Nicolaou, Savvas; Rowan, Kevin; Liu, David; Cunningham, Johan; Sargsyan, Ashot E.; Hamilton, Douglas; Dulchavsky, Scott A.
2005-05-01
The recent interest in the use of ultrasound (US) to detect pneumothoraces after acute trauma in North America was initially driven by an operational space medicine concern. Astronauts aboard the International Space Station (ISS) are at risk for pneumothoraces, and US is the only potential medical imaging available. Pneumothoraces are common following trauma, and are a preventable cause of death, as most are treatable with relatively simple interventions. While pneumothoraces are optimally diagnosed clinically, they are more often inapparent even on supine chest radiographs (CXR) with recent series reporting a greater than 50% rate of occult pneumothoraces. In the course of basic scientific investigations in a conventional and parabolic flight laboratory, investigators familiarized themselves with the sonographic features of both pneumothoraces and normal pulmonary ventilation. By examining the visceral-parietal pleural interface (VPPI) with US, investigators became confident in diagnosing pneumothoraces. This knowledge was subsequently translated into practice at an American and a Canadian trauma center. The sonographic examination was found to be more accurate and sensitive than CXR (US 96% and 100% versus US 74% and 36%) in specific circumstances. Initial studies have also suggested that detecting the US features of pleural pulmonary ventilation in the left lung field may offer the ability to exclude serious endotracheal tube malpositions such as right mainstem and esophageal intubations. Applied thoracic US is an example of a clinically useful space medicine spin-off that is improving health care on earth.
Radiation tolerance of a spin-dependent tunnelling magnetometer for space applications
Persson, Anders; Thornell, Greger; Nguyen, Hugo
2011-01-01
To meet the increasing demand for miniaturized space instruments, efforts have been made to miniaturize traditional magnetometers, e.g. fluxgate and spin-exchange relaxation-free magnetometers. These have, for different reasons, turned out to be difficult. New technologies are needed, and promising in this respect are tunnelling magnetoresistive (TMR) magnetometers, which are based on thin film technology. However, all new space devices first have to be qualified, particularly in terms of radiation resistance. A study on TMR magnetometers' vulnerability to radiation is crucial, considering the fact that they employ a dielectric barrier, which can be susceptible to charge trapping from ionizing radiation. Here, a TMR-based magnetometer, called the spin-dependent tunnelling magnetometer (SDTM), is presented. A magnetometer chip consisting of three Wheatstone bridges, with an angular pitch of 120°, was fabricated using microstructure technology. Each branch of the Wheatstone bridges consists of eight pairs of magnetic tunnel junctions (MTJs) connected in series. Two such chips are used to measure the three-dimensional magnetic field vector. To investigate the SDTM's resistance to radiation, one branch of a Wheatstone bridge was irradiated with gamma rays from a Co 60 source with a dose rate of 10.9 rad min −1 to a total dose of 100 krad. The TMR of the branch was monitored in situ, and the easy axis TMR loop and low-frequency noise characteristics of a single MTJ were acquired before and after irradiation with the total dose. It was concluded that radiation did not influence the MTJs in any noticeable way in terms of the TMR ratio, coercivity, magnetostatic coupling or low-frequency noise
Purely geometric path integral for spin-foams
Shirazi, Atousa Chaharsough; Engle, Jonathan
2014-01-01
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase—a topic of recent focus in spin-foams—but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski–Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued 2-form, called the Plebanski 2-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski 2-form alone. The spin-foam sum is therefore a discretized version of a Plebanski–Holst path integral in which only the Plebanski 2-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski–Holst path integral. In prior work in which one of the authors was involved, the measure factor for the Plebanski–Holst path integral with both connection and 2-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Background independence of the resulting path integral is discussed in the final section, and gauge-fixing is discussed in appendix B. (paper)
An anisotropic standing wave braneworld and associated Sturm-Liouville problem
Gogberashvili, Merab; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto
2012-01-01
We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy-momentum tensor components of the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm-Liouville problem associated with the correct localization condition of the transverse to the brane metric and scalar fields. It is shown that this condition restricts the physically meaningful space of solutions for the localization of the fluctuations of the model. (paper)
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
Gaiotto, D. [Institute for Advanced Study (IAS), Princeton, NJ (United States); Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-03-15
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S{sup 4}. (orig.)
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
Gaiotto, D.; Teschner, J.
2012-03-01
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S 4 . (orig.)
Zhidkov, P.E.
1996-01-01
First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs
Continuous spins in 2D gravity: Chiral vertex operators and local fields
Gervais, Jean-Loup; Schnittger, Jens
1994-01-01
We construct the exponentials of the Liouville field with continuous powers within the operator approach. Their chiral decomposition is realized using the explicit Coulomb-gas operators we introduced earlier. From the quantum group viewpoint, they are related to semi-infinite highest- or lowest-weight representations with continuous spins. The Liouville field itself is defined, and the canonical commutation relations are verified, as well as the validity of the quantum Liouville field equations. In a second part, both screening charges are considered. The braiding of the chiral components is derived and shown to agree with an ansatz of a parallel paper of Gervais and Roussel. ((orig.))
The Complex Spin State of 103P-Hartley 2: Kinematics and Orientation in Space
Belton, Michael J. S.; Thomas, Peter; Li, Jian-Yang; Williams, Jade; Carcich, Brian; A'Hearn, Michael F.; McLaughlin, Stephanie; Farnham, Tony; McFadden, Lucy; Lisse, Carey M.;
2013-01-01
We derive the spin state of the nucleus of Comet 103P/Hartley 2, its orientation in space, and its short-term temporal evolution from a mixture of observations taken from the DIXI (Deep Impact Extended Investigation) spacecraft and radar observations. The nucleus is found to spin in an excited long-axis mode (LAM) with its rotational angular momentum per unit mass, M, and rotational energy per unit mass, E, slowly decreasing while the degree of excitation in the spin increases through perihelion passage. M is directed toward (RA, Dec; J2000) = 8+/-+/- 4 deg., 54 +/- 1 deg. (obliquity = 48 +/- 1 deg.). This direction is likely changing, but the change is probably <6 deg. on the sky over the approx. 81.6 days of the DIXI encounter. The magnitudes of M and E at closest approach (JD 2455505.0831866 2011-11-04 13:59:47.310) are 30.0 +/- 0.2 sq. m/s and (1.56 +/- 0.02) X 10(exp -3) sq. m /sq. s respectively. The period of rotation about the instantaneous spin vector, which points in the direction (RA, Dec; J2000) = 300 +/- 3.2deg., 67 +/- 1.3 deg. at the time of closest approach, was 14.1 +/- 0.3 h. The instantaneous spin vector circulates around M, inclined at an average angle of 33.2 +/- 1.3 deg. with an average period of 18.40 +/- 0.13 h at the time of closest approach. The period of roll around the principal axis of minimum inertia (''long'' axis) at that time is 26.72 +/- 0.06 h. The long axis is inclined to M by approx. 81.2 +/- 0.6 deg. on average, slowly decreasing through encounter. We infer that there is a periodic nodding motion of the long axis with half the roll period, i.e., 13.36+/- 0.03 h, with amplitude of 1 again decreasing through encounter. The periodic variability in the circulation and roll rates during a cycle was at the 2% and 10-14% level respectively. During the encounter there was a secular lengthening of the circulation period of the long axis by 1.3 +/- 0.2 min/d, in agreement with ground-based estimates, while the period of roll around the
Integral-spin fields on (3+2)-de Sitter space
Gazeau, J.; Hans, M.
1988-01-01
Nowadays, (3+2)-de Sitter (or anti-de Sitter space) appears as a very attractive possibility at several levels of theoretical physics. The Wigner definition of an elementary system as associated to a unitary irreducible representation of the Poincare group may be extended to the de Sitter group SO(3,2) [or ∼(SO(3,2))] without great difficulty. The constant curvature, as small as it can be, is a natural candidate to play the role of a regularization parameter with respect to the flat-space limit. Massless particles in (3+2)-de Sitter theory are composite (singletons). On the other hand, supergravity theories necessitate a (large) constant curvature. The content of this paper is group theoretical. It attempts to continue the ''a la Wigner'' program for SO(3,2), already largely broached by Fronsdal. Three recurrence formulas are presented. They permit one to build up the carrier states for representations with arbitrary integral spin. Two of them are valid for the ''massive'' representations whereas the third one is applicable to the indecomposable massless representations. In addition, other presumably indecomposable, though nonphysical, representations are studied, in relation to the existence of ''generalized'' gauge fields and divergences. The recurrence formulas also allow one to build up the invariant two-point functions or homogeneous propagators
Fachruddin, Imam, E-mail: imam.fachruddin@sci.ui.ac.id; Salam, Agus [Departemen Fisika, Universitas Indonesia, Depok 16424 (Indonesia)
2016-03-11
A new momentum-space formulation for scattering of two spin-half particles, both either identical or unidentical, is formulated. As basis states the free linear-momentum states are not expanded into the angular-momentum states, the system’s spin states are described by the product of the spin states of the two particles, and the system’s isospin states by the total isospin states of the two particles. We evaluate the Lippmann-Schwinger equations for the T-matrix elements in these basis states. The azimuthal behavior of the potential and of the T-matrix elements leads to a set of coupled integral equations for the T-matrix elements in two variables only, which are the magnitude of the relative momentum and the scattering angle. Some symmetry relations for the potential and the T-matrix elements reduce the number of the integral equations to be solved. A set of six spin operators to express any interaction of two spin-half particles is introduced. We show the spin-averaged differential cross section as being calculated in terms of the solution of the set of the integral equations.
Schramm-Loewner evolution and Liouville quantum gravity.
Duplantier, Bertrand; Sheffield, Scott
2011-09-23
We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.
Twisting null geodesic congruences, scri, H-space and spin-angular momentum
Kozameh, Carlos; Newman, E T; Silva-Ortigoza, Gilberto
2005-01-01
The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat spacetime with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world line in a four-parameter complex space. Surprisingly, this parameter space turns out to be the H-space that is associated with the real physical spacetime under consideration. The main development in this work is the demonstration of how this complex world line can be made both unique and also given a physical meaning. More specifically, by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world line is uniquely determined and becomes (by several arguments) identified as the 'complex centre of mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum. One should think of this work as developing a generalization of the properties of the algebraically special spacetimes in the sense that the term that is forced here to vanish is automatically vanishing (among many other terms) for all the algebraically special metrics. This is demonstrated in the several given examples. It was, in fact, an understanding of the algebraically special metrics and their associated shear-free null congruence that led us to this construction of the asymptotically shear-free congruences and the unique complex world line. The Robinson-Trautman metrics and the Kerr and charged Kerr metrics with their properties are explicit examples of the construction given here
Integrability of Liouville system on high genus Riemann surface: Pt. 1
Chen Yixin; Gao Hongbo
1992-01-01
By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface
Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)
Shen Jianmin; Sheng Zhengmao; Wang Zhonghua
1992-02-01
We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs
Weigert, S.
1999-01-01
To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after inverting the experimental data, the statistical operator is parametrized entirely by expectation values. On this basis, a symbolic calculus for quantum spins is developed, the e xpectation-value representation . It resembles the Moyal representation for SU(2) but two important differences exist. On the one hand, the symbols take values on a discrete set of points in phase space only. On the other hand, no quasi-probabilities - that is, phase-space distributions with negative values - are encountered in this approach. (Author)
Liouville and Painleve equations and Yang--Mills strings
Saclioglu, C.K.
1984-01-01
Stringlike solutions of the self-dual Yang--Mills equations (dimensionally reduced to R 2 ) are sought. A multistring Ansatz results in the sinh--Gordon and Liouville equations. According to a general theorem, the solutions must be either real and singular and have infinite action, or complex and nonsingular, with zero action. In the Liouville case, explicit arbitrarily separated n-string solutions of both classes are given. The magnetic flux for these solutions is found to be the Chern class of a Kaehler manifold, and it consequently assumes quantized values 4πn/e. The axisymmetric version of the sinh--Gordon is solved by the third Painleve transcendent P 3 , using the results on P 3 by Wu et al. [Phys. Rev. B 13, 316 (1976)] and McCoy et al. [J. Math. Phys. 18, 10 (1977)]. The axisymmetric case can be cast into the Ernst equation framework for the generation of further solutions. In the Appendix, the Euclideanized Ernst equation is shown to give self-dual Gibbons--Hawking gravitational instantons
WKB analysis of PT-symmetric Sturm–Liouville problems
Bender, Carl M; Jones, Hugh F
2012-01-01
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schrödinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the case with regular Hermitian Sturm–Liouville problems, the eigenvalues of the PT-symmetric Sturm–Liouville problem grow like n 2 for large n. However, the novelty is that a PT eigenvalue problem on a finite domain typically exhibits a sequence of critical points at which pairs of eigenvalues cease to be real and become complex conjugates of one another. For the potentials considered here this sequence of critical points is associated with a turning point on the imaginary axis in the complex plane. WKB analysis is used to calculate the asymptotic behaviours of the real eigenvalues and the locations of the critical points. The method turns out to be surprisingly accurate even at low energies. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)
Correlation functions in unitary minimal Liouville gravity and Frobenius manifolds
Belavin, V. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Department of Theoretical Physics, National Research Nuclear University MEPhI,Kashirskoe shosse 31, 115409 Moscow (Russian Federation)
2015-02-10
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A{sub q} integrable hierarchy via the resonance transformations, which are in turn fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.
Isomonodromic tau-functions from Liouville conformal blocks
Iorgov, N.; Lisovyy, O.
2014-01-01
The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c=1. This implies a similar representation for the isomonodromic tau-function. In the case n=4 we thereby get a proof of the relation between tau-functions and conformal blocks discovered in O. Gamayun, N. Iorgov, and O. Lisovyy (2012). We briefly discuss a possible application of our results to the study of relations between certain N=2 supersymmetric gauge theories and conformal field theory.
Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics
1977-06-27
Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.
Real-Space Application of the Mean-Field Description of Spin-Glass Dynamics
Barrat, Alain; Berthier, Ludovic
2001-01-01
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard 'mean-field theory' versus 'droplet picture' debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed
Spectral theory of Sturm-Liouville differential operators: proceedings of the 1984 workshop
Kaper, H.G.; Zettl, A. (eds.)
1984-12-01
This report contains the proceedings of the workshop which was held at Argonne during the period May 14 through June 15, 1984. The report contains 22 articles, authored or co-authored by the participants in the workshop. Topics covered at the workshop included the asymptotics of eigenvalues and eigenfunctions; qualitative and quantitative aspects of Sturm-Liouville eigenvalue problems with discrete and continuous spectra; polar, indefinite, and nonselfadjoint Sturm-Liouville eigenvalue problems; and systems of differential equations of Sturm-Liouville type.
STM Studies of Spin-Orbit Coupled Phases in Real- and Momentum-Space
Madhavan, Vidya [Univ. of Illinois, Urbana, IL (United States)
2016-10-17
The recently discovered class of spin-orbit coupled materials with interesting topological character are fascinating both from fundamental as well as application point of view. Two striking examples are 3D topological insulators (TIs) and topological crystalline insulators (TCIs). These materials host linearly dispersing (Dirac like) surface states with an odd number of Dirac nodes and are predicted to carry a quantized half-integer value of the axion field. The non-trivial topological properties of TIs and TCIs arise from strong spin-orbit coupling leading to an inverted band structure; which also leads to the chiral spin texture in momentum space. In this project we used low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to study materials with topological phases in real- and momentum-space. We studied both single crystals and thin films of topological materials which are susceptible to being tuned by doping, strain or gating, allowing us to explore their physical properties in the most interesting regimes and set the stage for future technological applications. .
Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G2-structure
Haupt, Alexander S.
2016-01-01
We study g-valued Yang-Mills fields on cylinders Z(G/H)=ℝ×G/H, where G/H is a compact seven-dimensional coset space with G 2 -structure, g is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in ℝ n under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel G 2 -structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.
Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
Zhu, Chengcheng; Tian, Bing; Chen, Luguang; Eisenmenger, Laura; Raithel, Esther; Forman, Christoph; Ahn, Sinyeob; Laub, Gerhard; Liu, Qi; Lu, Jianping; Liu, Jing; Hess, Christopher; Saloner, David
2018-06-01
Develop and optimize an accelerated, high-resolution (0.5 mm isotropic) 3D black blood MRI technique to reduce scan time for whole-brain intracranial vessel wall imaging. A 3D accelerated T 1 -weighted fast-spin-echo prototype sequence using compressed sensing (CS-SPACE) was developed at 3T. Both the acquisition [echo train length (ETL), under-sampling factor] and reconstruction parameters (regularization parameter, number of iterations) were first optimized in 5 healthy volunteers. Ten patients with a variety of intracranial vascular disease presentations (aneurysm, atherosclerosis, dissection, vasculitis) were imaged with SPACE and optimized CS-SPACE, pre and post Gd contrast. Lumen/wall area, wall-to-lumen contrast ratio (CR), enhancement ratio (ER), sharpness, and qualitative scores (1-4) by two radiologists were recorded. The optimized CS-SPACE protocol has ETL 60, 20% k-space under-sampling, 0.002 regularization factor with 20 iterations. In patient studies, CS-SPACE and conventional SPACE had comparable image scores both pre- (3.35 ± 0.85 vs. 3.54 ± 0.65, p = 0.13) and post-contrast (3.72 ± 0.58 vs. 3.53 ± 0.57, p = 0.15), but the CS-SPACE acquisition was 37% faster (6:48 vs. 10:50). CS-SPACE agreed with SPACE for lumen/wall area, ER measurements and sharpness, but marginally reduced the CR. In the evaluation of intracranial vascular disease, CS-SPACE provides a substantial reduction in scan time compared to conventional T 1 -weighted SPACE while maintaining good image quality.
Minimal Liouville gravity on the torus via the Douglas string equation
Spodyneiko, Lev
2015-01-01
In this paper we assume that the partition function in minimal Liouville gravity (MLG) obeys the Douglas string equation. This conjecture makes it possible to compute the torus correlation numbers in (3,p) MLG. We perform this calculation using also the resonance relations between the coupling constants in the KdV frame and in the Liouville frame. We obtain explicit expressions for the torus partition function and for the one- and two-point correlation numbers. (paper)
Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s
Ming Li
2013-01-01
Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.
Hershey, Matthew P.; Newswander, Daniel R.; Smith, James P.; Lamb, Craig R.; Ballard, Perry G.
2015-01-01
The Space Station Integrated Kinetic Launcher for Orbital Payload Systems (SSIKLOPS), known as "Cyclops" to the International Space Station (ISS) community, successfully deployed the largest satellite ever (SpinSat) from the ISS on November 28, 2014. Cyclops, a collaboration between the NASA ISS Program, NASA Johnson Space Center Engineering, and Department of Defense Space Test Program (DoD STP) communities, is a dedicated 10-100 kg class ISS small satellite deployment system. This paper will showcase the successful deployment of SpinSat from the ISS. It will also outline the concept of operations, interfaces, requirements, and processes for satellites to utilize the Cyclops satellite deployment system.
Altahawi, Faysal F.; Blount, Kevin J.; Omar, Imran M. [Northwestern University Feinberg School of Medicine, Department of Radiology, Chicago, IL (United States); Morley, Nicholas P. [Marshfield Clinic, Department of Radiology, Marshfield, WI (United States); Raithel, Esther [Siemens Healthcare GmbH, Erlangen (Germany)
2017-01-15
To compare a faster, new, high-resolution accelerated 3D-fast-spin-echo (3D-FSE) acquisition sequence (CS-SPACE) to traditional 2D and high-resolution 3D sequences for knee 3-T magnetic resonance imaging (MRI). Twenty patients received knee MRIs that included routine 2D (T1, PD ± FS, T2-FS; 0.5 x 0.5 x 3 mm{sup 3}; ∝10 min), traditional 3D FSE (SPACE-PD-FS; 0.5 x 0.5 x 0.5 mm{sup 3}; ∝7.5 min), and accelerated 3D-FSE prototype (CS-SPACE-PD-FS; 0.5 x 0.5 x 0.5 mm{sup 3}; ∝5 min) acquisitions on a 3-T MRI system (Siemens MAGNETOM Skyra). Three musculoskeletal radiologists (MSKRs) prospectively and independently reviewed the studies with graded surveys comparing image and diagnostic quality. Tissue-specific signal-to-noise ratios (SNR) and contrast-to-noise ratios (CNR) were also compared. MSKR-perceived diagnostic quality of cartilage was significantly higher for CS-SPACE than for SPACE and 2D sequences (p < 0.001). Assessment of diagnostic quality of menisci and synovial fluid was higher for CS-SPACE than for SPACE (p < 0.001). CS-SPACE was not significantly different from SPACE but had lower assessments than 2D sequences for evaluation of bones, ligaments, muscles, and fat (p ≤ 0.004). 3D sequences had higher spatial resolution, but lower overall assessed contrast (p < 0.001). Overall image quality from CS-SPACE was assessed as higher than SPACE (p = 0.007), but lower than 2D sequences (p < 0.001). Compared to SPACE, CS-SPACE had higher fluid SNR and CNR against all other tissues (all p < 0.001). The CS-SPACE prototype allows for faster isotropic acquisitions of knee MRIs over currently used protocols. High fluid-to-cartilage CNR and higher spatial resolution over routine 2D sequences may present a valuable role for CS-SPACE in the evaluation of cartilage and menisci. (orig.)
Exploring the local conformational space of a membrane protein by site-directed spin labeling
Stopar, D.; Strancar, J.; Spruijt, R.B.; Hemminga, M.A.
2005-01-01
Molecular modeling based on a hybrid evolutionary optimization and an information condensation algorithm, called GHOST, of spin label ESR spectra was applied to study the structure and dynamics of membrane proteins. The new method is capable of providing detailed molecular information about the
Gazoya, E.D.K.; Prempeh, E.; Banini, G.K.
2015-01-01
The relationship between the spin transformations of the special linear group of order 2, SL (2, C) and the aggregate SO(3) of the three-dimensional pure rotations when considered as a group in itself (and not as a subgroup of the Lorentz group), is investigated. It is shown, by the spinor map X - → AXA ct which is all action of SL(2. C) on the space of Hermitian matrices, that the one- parameter subgroup of rotations generated are precisely those of angles which are multiples 2π. (au)
Burtnyak Ivan V.
2017-06-01
Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.
2017-12-01
In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.
Gridneva, S.A.; Rus'kin, V.I.
1980-01-01
Basic features of the statistical model of multiple hadron production based on microcanonical distribution and taking into account the laws of conservation of total angular momentum, isotopic spin, p-, G-, C-eveness and Bose-Einstein statistics requirements are given. The model predictions are compared with experimental data on anti NN annihilation at rest and e + e - annihilation in hadrons at annihilation total energy from 2 to 3 GeV [ru
Classical and statistical mechanics of celestial-scale spinning strings: Rotating space elevators
Golubović, L.; Knudsen, S.
2009-05-01
We introduce novel and unique class of dynamical systems, Rotating Space Elevators (RSE). The RSEs are multiply rotating systems of strings reaching into outer space. Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. The RSEs exhibit interesting nonlinear dynamics and statistical physics phenomena.
Deformed type 0A matrix model and super-Liouville theory for fermionic black holes
Ahn, Changrim; Kim, Chanju; Park, Jaemo; Suyama, Takao; Yamamoto, Masayoshi
2006-01-01
We consider a c-circumflex = 1 model in the fermionic black hole background. For this purpose we consider a model which contains both the N 1 and the N = 2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N = 2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N = 2 super-Liouville theory when the N = 1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary n-point correlation functions of the N = 1 super-Liouville theory on the sphere
Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath
Ajoy, Ashok; Alvarez, Gonzalo A.; Suter, Dieter
2011-01-01
Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses [the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence [the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are 13 C nuclear spins and the environment consists of a 1 H nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.
Afzali, R., E-mail: afzali@kntu.ac.ir [Department of Physics, K. N. Toosi University of Technology, Tehran, 15418 (Iran, Islamic Republic of); Ebrahimian, N., E-mail: n.ebrahimian@shahed.ac.ir [Department of Physics, Faculty of Basic Sciences, Shahed University, Tehran, 18155-159 (Iran, Islamic Republic of); Eghbalifar, B., E-mail: b.eghbali2011@yahoo.com [Department of Agricultural Management, Marvdasht Branch, Azad University, Marvdasht (Iran, Islamic Republic of)
2016-10-07
Highlights: • In contrast to a s-wave superconductor, the quantum correlation of the d-wave superconductor is sensitive to the change of the gap magnitude. • Quantum discord of the d-wave superconductor oscillates. • Quantum discord becomes zero at a characteristic length of the d-wave superconductor. • Quantum correlation strongly depends on the length of grain. Length of the superconductor lower, the quantum correlation length higher. • Quantum tripartite entanglement for a nano-scale d-wave superconductor is better than for a bulk d-wave superconductor. - Abstract: By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.
Kunito Fukuda
2017-08-01
Full Text Available Spin-dependent space-charge-limited carrier conduction in a Schottky barrier diode using polycrystalline p-type π-conjugated molecular pentacene is explored using multiple-frequency electrically detected magnetic resonance (EDMR spectroscopy with a variable-angle configuration. The measured EDMR spectra are decomposed into two components derived, respectively, from mobile and trapped positive polarons. The linewidth of the EDMR signal for the trapped polarons increases with increasing resonance magnetic field for an in-plane configuration where the normal vector of the device substrate is perpendicular to the resonance magnetic field, while it is independent of the field for an out-of-plane configuration. This difference is consistent with the pentacene arrangement on the device substrate, where pentacene molecules exhibit a uniaxial orientation on the out-of-substrate plane. By contrast, the mobile polarons do not show anisotropic behavior with respect to the resonance magnetic field, indicating that the anisotropic effect is averaged out owing to carrier motion. These results suggest that the orientational arrangements of polycrystalline pentacene molecules in a nano thin film play a crucial role in spin-dependent electrical conduction.
Fukuda, Kunito; Asakawa, Naoki
2017-08-01
Spin-dependent space charge limited carrier conduction in a Schottky barrier diode using polycrystalline p-type π-conjugated molecular pentacene is explored using multiple-frequency electrically detected magnetic resonance (EDMR) spectroscopy with a variable-angle configuration. The measured EDMR spectra are decomposed into two components derived respectively from mobile and trapped positive polarons. The linewidth of the EDMR signal for the trapped polarons increases with increasing resonance magnetic field for an in-plane configuration where the normal vector of the device substrate is perpendicular to the resonance magnetic field, while it is independent of the field for an out-of-plane configuration. This difference is consistent with the pentacene arrangement on the device substrate, where pentacene molecules exhibit a uniaxial orientation on the out-of-substrate plane. By contrast, the mobile polarons do not show anisotropic behavior with respect to the resonance magnetic field, indicating that the anisotropic effect is averaged out owing to carrier motion. These results suggest that the orientational arrangements of polycrystalline pentacene molecules in a nano thin film play a crucial role in spin-dependent electrical conduction.
Entangled spins and ghost-spins
Dileep P. Jatkar
2017-09-01
Full Text Available We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in [20] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves, the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the ghost-spins. With an odd number of ghost-spins however, we find that there always exist positive norm states with negative real part for entanglement entropy after tracing over the ghost-spins.
Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations
Xu Xixiang
2012-01-01
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)
Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation
Zecca, A.
2010-01-01
The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.
Geometry of spin coherent states
Chryssomalakos, C.; Guzmán-González, E.; Serrano-Ensástiga, E.
2018-04-01
Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many respects, the ‘most classical’ available. For any spin s, the spin coherent states form a 2-sphere in the projective Hilbert space \
Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Spinning, hurting, still, afraid: Living life spaces with Type I Chiari Malformation.
Andrews, Gavin J
2018-01-31
Human geography's varied engagement with the brain has involved considerations of the way people know and respond to their environments, and their place-based experiences with emotions, mental illnesses and disorders, intellectual disabilities and particular neurological conditions. This paper argues however that this scholarship could be augmented by, and existing expertise be directed towards, considering physical brain abnormalities and injuries. As a case in point it considers the spatial experience of living with Type 1 Chiari Malformation. Through interviews with four sufferers, the research articulates three domains that they have had to re-negotiate - home space, social space and medical space - emphasizing supportive and challenging aspects of each, as well as meaningful and affective qualities to encounters. The paper concludes with some pointers towards the future study of physical brain abnormalities and injuries and the kinds of knowledge it might create to increase awareness and inform care. Copyright © 2018 Elsevier Ltd. All rights reserved.
Cornelis van der Mee
2005-01-01
Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian
Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems
Vanden Berghe, G.; Van Daele, M.; De Meyer, H.
1994-01-01
A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))
Half-linear Sturm-Liouville problem with weights: asymptotic behavior of eigenfunctions
Drábek, P.; Kufner, Alois; Kuliev, K.
2014-01-01
Roč. 284, č. 1 (2014), s. 148-154 ISSN 0081-5438 Institutional support: RVO:67985840 Keywords : Sturm-Liouville problem * spectral problems * Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.302, year: 2014 http://link.springer.com/article/10.1134%2FS008154381401009X
Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.
2015-01-01
We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or
X-ray Pulsars Across the Parameter Space of Luminosity, Accretion Mode, and Spin
Laycock, Silas
We propose to expand the scope of our successful project providing a multi-satellite library of X-ray Pulsar observations to the community. The library provides high-level products, activity monitoring, pulse-profiles, phased event files, spectra, and a unique pulse-profile modeling interface. The library's scientific footprint will expand in 4 key directions: (1) Update, by processing all new XMM-Newton and Chandra observations (2015-2017) of X-ray Binary Pulsars in the Magellanic Clouds. (2) Expand, by including all archival Suzaku, Swift and NuStar observations, and including Galactic pulsars. (3) Improve, by offering innovative data products that provide deeper insight. (4) Advance, by implementing a new generation of physically motivated emission and pulse-profile models. The library currently includes some 2000 individual RXTE-PCA, 200 Chandra ACIS-I, and 120 XMM-PN observations of the SMC spanning 15 years, creating an unrivaled record of pulsar temporal behavior. In Phase-2, additional observations of SMC pulsars will be added: 221 Chandra (ACIS-S and ACIS-I), 22 XMM-PN, 142 XMM-MOS, 92 Suzaku, 25 NuSTAR, and >10,000 Swift; leveraging our pipeline and analysis techniques already developed. With the addition of 7 Galactic pulsars each having many hundred multisatellite observations, these datasets cover the entire range of variability timescales and accretion regimes. We will model the pulse-profiles using state of the art techniques to parameterize their morphology and obtain the distribution of offsets between magnetic and spin axes, and create samples of profiles under specific accretion modes (whether pencil-beam or fan-beam dominated). These products are needed for the next generation of advances in neutron star theory and modeling. The long-duration of the dataset and “whole-galaxy" nature of the SMC sample make possible a new statistical approach to uncover the duty-cycle distribution and hence population demographics of transient High Mass X
Mayhall, Nicholas J.; Head-Gordon, Martin
2014-01-01
An approximation to the spin-flip extended configuration interaction singles method is developed using a second-order perturbation theory approach. In addition to providing significant efficiency advantages, the new framework is general for an arbitrary number of spin-flips, with the current implementation being applicable for up to around 4 spin-flips. Two new methods are introduced: one which is developed using non-degenerate perturbation theory, spin-flip complete active-space (SF-CAS(S)), and a second quasidegenerate perturbation theory method, SF-CAS(S) 1 . These two approaches take the SF-CAS wavefunction as the reference, and then perturbatively includes the effect of single excitations. For the quasidegenerate perturbation theory method, SF-CAS(S) 1 , the subscripted “1” in the acronym indicates that a truncated denominator expansion is used to obtain an energy-independent down-folded Hamiltonian. We also show how this can alternatively be formulated in terms of an extended Lagrangian, by introducing an orthonormality constraint on the first-order wavefunction. Several numerical examples are provided, which demonstrate the ability of SF-CAS(S) and SF-CAS(S) 1 to describe bond dissociations, singlet-triplet gaps of organic molecules, and exchange coupling parameters for binuclear transition metal complexes
Parametric instability of spinning elastic rings excited by fluctuating space-fixed stiffnesses
Liu, Chunguang; Cooley, Christopher G.; Parker, Robert G.
2017-07-01
This study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space-fixed discrete stiffnesses with periodically fluctuating stiffnesses. The rotating, elastic ring is modeled using thin-ring theory with radial and tangential deformations. Primary and combination instability regions are determined in closed-form using the method of multiple scales. The ratio of peak-to-peak fluctuation to average discrete stiffness is used as the perturbation parameter, so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses. The natural frequencies and vibration modes are determined by discretizing the governing equations using Galerkin's method. Results are demonstrated for compliant gear applications. The perturbation results are validated by direct numerical integration of the equations of motion and Floquet theory. The bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses. For rings with multiple discrete stiffnesses, the phase differences between them can eliminate large amplitude response under certain conditions.
Meckler, S; Mikuszeit, N; Pressler, A; Vedmedenko, E Y; Pietzsch, O; Wiesendanger, R
2009-10-09
Using spin-polarized scanning tunneling microscopy performed in a triple axes vector magnet, we show that the magnetic structure of the Fe double layer on W(110) is an inhomogeneous right-rotating cycloidal spin spiral. The magnitude of the Dzyaloshinskii-Moriya vector is extracted from the experimental data using micromagnetic calculations. The result is confirmed by comparison of the measured saturation field along the easy axis to the respective value as obtained from Monte Carlo simulations. We find that the Dzyaloshinskii-Moriya interaction is too weak to destabilize the single domain state. However, it can define the sense of rotation and the cycloidal spiral type once the single domain state is destabilized by dipolar interaction.
Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations
Godinho, Cresus F.L.; Weberszpil, J.; Helayël-Neto, J.A.
2012-01-01
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.
Beam phase space and emittance
Buon, J.
1990-12-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation and to treat two particular examples
H{sup +}{sub 3} WZNW model from Liouville field theory
Hikida, Y.; Schomerus, V.
2007-06-15
There exists an intriguing relation between genus zero correlation functions in the H{sup +}{sub 3} WZNW model and in Liouville field theory. This was found by Ribault and Teschner based in part on earlier ideas by Stoyanovsky. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program. (orig.)
Xia Tiecheng; Chen Xiaohong; Chen Dengyuan
2004-01-01
An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations
Sectors of solutions and minimal energies in classical Liouville theories for strings
Johansson, L.; Kihlberg, A.; Marnelius, R.
1984-01-01
All classical solutions of the Liouville theory for strings having finite stable minimum energies are calculated explicitly together with their minimal energies. Our treatment automatically includes the set of natural solitonlike singularities described by Jorjadze, Pogrebkov, and Polivanov. Since the number of such singularities is preserved in time, a sector of solutions is not only characterized by its boundary conditions but also by its number of singularities. Thus, e.g., the Liouville theory with periodic boundary conditions has three different sectors of solutions with stable minimal energies containing zero, one, and two singularities. (Solutions with more singularities have no stable minimum energy.) It is argued that singular solutions do not make the string singular and therefore may be included in the string quantization
Higher equations of motion in N=2 superconformal Liouville field theory
Ahn, Changrim; Stanishkov, Marian; Stoilov, Michail
2011-01-01
We present an infinite set of higher equations of motion in N=2 supersymmetric Liouville field theory. They are in one to one correspondence with the degenerate representations and are enumerated in addition to the U(1) charge ω by the positive integers m or (m,n) respectively. We check that in the classical limit these equations hold as relations among the classical fields.
Schulze-Halberg, Axel
2010-01-01
We study Green's functions of the generalized Sturm-Liouville problems that are related to each other by Darboux -equivalently, supersymmetrical - transformations. We establish an explicit relation between the corresponding Green's functions and derive a simple formula for their trace. The class of equations considered here includes the conventional Schroedinger equation and generalizations, such as for position-dependent mass and with linearly energy-dependent potential, as well as the stationary Fokker-Planck equation.
Memoria sobre el papel de Liouville en la historia de las funciones elípticas
Leonardo Solanilla Chavarro
2014-06-01
Full Text Available Este artículo recoge las principales conclusiones de una investigación sobre las contribuciones de J. Liouville a la teoría contemporánea de las funciones elípticas. Cubre la mayor parte de los resultados de una colaboración entre el grupo SUMMA del Departamento de Ciencias Básicas de la Universidad de Medellín y el grupo Mat del Departamento de Matemáticas y Estadística de la Universidad del Tolima. El proyecto ha sido financiado parcialmente por la Vicerrectoría de Investigaciones de la Universidad de Medellín y la Facultad de Ciencias de la Universidad del Tolima. Comienza con una descripción de la circunstancia histórica de Liouville, luego de la emergencia del concepto moderno de función elíptica en los trabajos de Abel y Jacobi. Después se discuten ciertos pormenores de las Leçons impartidas por el célebre matemático francés en el año de 1847. Ellos cubren el teorema que hemos llamado de Liouville-Borchardt, las proposiciones fundamentales sobre el número de ceros de las funciones meromorfas doblemente periódicas y los resultados sobre la relación entre los ceros y los polos. Al final, se esbozan importantes conclusiones sobre el legado de Liouville a la teoría de las funciones elípticas de hoy.
Comments on fusion matrix in N=1 super Liouville field theory
Hasmik Poghosyan
2016-08-01
Full Text Available We study several aspects of the N=1 super Liouville theory. We show that certain elements of the fusion matrix in the Neveu–Schwarz sector are related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy–Lewellen equation for defects is studied, and defects are constructed.
The Euler anomaly and scale factors in Liouville/Toda CFTs
Balasubramanian, Aswin [Theory Group, Department of Physics, University of Texas at Austin,2515 Speedway Stop C1608, Austin, TX 78712-1197 (United States)
2014-04-22
The role played by the Euler anomaly in the dictionary relating sphere partition functions of four dimensional theories of class S and two dimensional non rational CFTs is clarified. On the two dimensional side, this involves a careful treatment of scale factors in Liouville/Toda correlators. Using ideas from tinkertoy constructions for Gaiotto duality, a framework is proposed for evaluating these scale factors. The representation theory of Weyl groups plays a critical role in this framework.
Hsieh, Chang-Yu; Kapral, Raymond
2013-01-01
Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined j...
Fan, Wentao; Bouguila, Nizar
2013-11-01
A large class of problems can be formulated in terms of the clustering process. Mixture models are an increasingly important tool in statistical pattern recognition and for analyzing and clustering complex data. Two challenging aspects that should be addressed when considering mixture models are how to choose between a set of plausible models and how to estimate the model's parameters. In this paper, we address both problems simultaneously within a unified online nonparametric Bayesian framework that we develop to learn a Dirichlet process mixture of Beta-Liouville distributions (i.e., an infinite Beta-Liouville mixture model). The proposed infinite model is used for the online modeling and clustering of proportional data for which the Beta-Liouville mixture has been shown to be effective. We propose a principled approach for approximating the intractable model's posterior distribution by a tractable one-which we develop-such that all the involved mixture's parameters can be estimated simultaneously and effectively in a closed form. This is done through variational inference that enjoys important advantages, such as handling of unobserved attributes and preventing under or overfitting; we explain that in detail. The effectiveness of the proposed work is evaluated on three challenging real applications, namely facial expression recognition, behavior modeling and recognition, and dynamic textures clustering.
Hodel, Jerome [Unite Analyse et Restauration du Mouvement, UMR-CNRS, 8005 LBM ParisTech Ensam, Paris (France); University Paris Est Creteil (UPEC), Creteil (France); Assistance Publique-Hopitaux de Paris, Paris (France); Hopital Henri Mondor, Department of Neuroradiology, Creteil (France); Hopital Henri Mondor, Creteil (France); Silvera, Jonathan [University Paris Est Creteil (UPEC), Creteil (France); Assistance Publique-Hopitaux de Paris, Paris (France); Hopital Henri Mondor, Department of Neuroradiology, Creteil (France); Bekaert, Olivier; Decq, Philippe [Unite Analyse et Restauration du Mouvement, UMR-CNRS, 8005 LBM ParisTech Ensam, Paris (France); University Paris Est Creteil (UPEC), Creteil (France); Assistance Publique-Hopitaux de Paris, Paris (France); Hopital Henri Mondor, Department of Neurosurgery, Creteil (France); Rahmouni, Alain [University Paris Est Creteil (UPEC), Creteil (France); Assistance Publique-Hopitaux de Paris, Paris (France); Hopital Henri Mondor, Department of Radiology, Creteil (France); Bastuji-Garin, Sylvie [University Paris Est Creteil (UPEC), Creteil (France); Assistance Publique-Hopitaux de Paris, Paris (France); Hopital Henri Mondor, Department of Public Health, Creteil (France); Vignaud, Alexandre [Siemens Healthcare, Saint Denis (France); Petit, Eric; Durning, Bruno [Laboratoire Images Signaux et Systemes Intelligents, UPEC, Creteil (France)
2011-02-15
To assess the three-dimensional turbo spin echo with variable flip-angle distribution magnetic resonance sequence (SPACE: Sampling Perfection with Application optimised Contrast using different flip-angle Evolution) for the imaging of intracranial cerebrospinal fluid (CSF) spaces. We prospectively investigated 18 healthy volunteers and 25 patients, 20 with communicating hydrocephalus (CH), five with non-communicating hydrocephalus (NCH), using the SPACE sequence at 1.5T. Volume rendering views of both intracranial and ventricular CSF were obtained for all patients and volunteers. The subarachnoid CSF distribution was qualitatively evaluated on volume rendering views using a four-point scale. The CSF volumes within total, ventricular and subarachnoid spaces were calculated as well as the ratio between ventricular and subarachnoid CSF volumes. Three different patterns of subarachnoid CSF distribution were observed. In healthy volunteers we found narrowed CSF spaces within the occipital aera. A diffuse narrowing of the subarachnoid CSF spaces was observed in patients with NCH whereas patients with CH exhibited narrowed CSF spaces within the high midline convexity. The ratios between ventricular and subarachnoid CSF volumes were significantly different among the volunteers, patients with CH and patients with NCH. The assessment of CSF spaces volume and distribution may help to characterise hydrocephalus. (orig.)
Hodel, Jerome; Silvera, Jonathan; Bekaert, Olivier; Decq, Philippe; Rahmouni, Alain; Bastuji-Garin, Sylvie; Vignaud, Alexandre; Petit, Eric; Durning, Bruno
2011-01-01
To assess the three-dimensional turbo spin echo with variable flip-angle distribution magnetic resonance sequence (SPACE: Sampling Perfection with Application optimised Contrast using different flip-angle Evolution) for the imaging of intracranial cerebrospinal fluid (CSF) spaces. We prospectively investigated 18 healthy volunteers and 25 patients, 20 with communicating hydrocephalus (CH), five with non-communicating hydrocephalus (NCH), using the SPACE sequence at 1.5T. Volume rendering views of both intracranial and ventricular CSF were obtained for all patients and volunteers. The subarachnoid CSF distribution was qualitatively evaluated on volume rendering views using a four-point scale. The CSF volumes within total, ventricular and subarachnoid spaces were calculated as well as the ratio between ventricular and subarachnoid CSF volumes. Three different patterns of subarachnoid CSF distribution were observed. In healthy volunteers we found narrowed CSF spaces within the occipital aera. A diffuse narrowing of the subarachnoid CSF spaces was observed in patients with NCH whereas patients with CH exhibited narrowed CSF spaces within the high midline convexity. The ratios between ventricular and subarachnoid CSF volumes were significantly different among the volunteers, patients with CH and patients with NCH. The assessment of CSF spaces volume and distribution may help to characterise hydrocephalus. (orig.)
Allen, Philip B.; Pickett, Warren E.
2018-06-01
Since closed lines of accidental electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material - aluminum - is recounted and elaborated on. Nodal loop semimetals have become a focus of recent activity, with emphasis on other issues. Band degeneracies are, after all, the origin of topological phases in crystalline materials. Spin-orbit interaction lifts accidental band degeneracies, with the resulting spectrum being provided here. The geometric phase γ(C) = ± π for circuits C surrounding a line of such degeneracy cannot survive completely unchanged. The change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, γ(C) decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and γ(C) = ± π is unchanged.
Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi
2018-06-01
The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.
Physical States and BRST Operators for Higher-spin $W$ Strings
Liu, Yu-Xiao; Wei, Shao-Wen; Zhang, Li-Jie; Ren, Ji-Rong
2008-01-01
In this paper, we mainly investigate the $W_{2,s}^{M}\\otimes W_{2,s}^{L}$ system, in which the matter and the Liouville subsystems generate $W_{2,s}^{M}$ and $W_{2,s}^L$ algebras respectively. We first give a brief discussion of the physical states for corresponding $W$ stings. The lower states are given by freezing the spin-2 and spin-$s$ currents. Then, introducing two pairs of ghost-like fields, we give the realizations of $W_{1,2,s}$ algebras. Based on these linear realizations, BRST oper...
Guseinov, I.I.
2007-01-01
The new analytical relations of complete orthonormal sets for the tensor wave functions and the tensor Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces are derived using the properties of tensor spherical harmonics and complete orthonormal scalar basis sets of ψ α -exponential type orbitals, φ α -momentum space orbitals and z α -hyperspherical harmonics introduced by the author for particles with spin s=0, where the α=1,0,-1,-2,.... All of the tensor wave functions obtained are complete without the inclusion of the continuum and, therefore, their group of transformations is the four-dimensional rotation group O(4). The analytical formulas in coordinate space are also derived for the overlap integrals over tensor Slater orbitals with the same screening constant. We notice that the new idea presented in this work is the combination of tensor spherical harmonics of rank s with complete orthonormal scalar sets for radial parts of ψ α -, φ α - and z α -orbitals, where s=1/2,1,3/2,2,...
A bifurcation result for Sturm-Liouville problems with a set-valued term
Georg Hetzer
1998-11-01
Full Text Available It is established in this note that $-(ku''+g(cdot,uin mu F(cdot,u$, $u'(0=0=u'(1$, has a multiple bifurcation point at $ (0, 0}$ in the sense that infinitely many continua meet at $(0,0$. $F$ is a ``set-valued representation'' of a function with jump discontinuities along the line segment $[0,1]imes{0}$. The proof relies on a Sturm-Liouville version of Rabinowitz's bifurcation theorem and an approximation procedure.
Duality and the Knizhnik-Polyakov-Zamolodchikov relation in Liouville quantum gravity.
Duplantier, Bertrand; Sheffield, Scott
2009-04-17
We present a (mathematically rigorous) probabilistic and geometrical proof of the Knizhnik-Polyakov-Zamolodchikov relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gravity. It uses the properly regularized quantum area measure dmicro_{gamma}=epsilon;{gamma;{2}/2}e;{gammah_{epsilon}(z)}dz, where dz is the Lebesgue measure on D, gamma is a real parameter, 02 is shown to be related to the quantum measure dmu_{gamma;{'}}, gamma;{'}<2, by the fundamental duality gammagamma;{'}=4.
Remarks on the Liouville type results for the compressible Navier–Stokes equations in RN
Chae, Dongho
2012-01-01
In this paper, we prove Liouville type result for the stationary solutions to the compressible Navier–Stokes equations (NS) and the compressible Navier–Stokes–Poisson (NSP) equations and in R N , N ≥ 2. Assuming suitable integrability and the uniform boundedness conditions for the solutions we are led to the conclusion that v = 0. In the case of (NS) we deduce that the similar integrability conditions imply v = 0 and ρ = constant on R N . This shows that if we impose the the non-vacuum boundary condition at spatial infinity for (NS), v → 0 and ρ → ρ ∞ > 0, then v = 0, ρ = ρ ∞ are the solutions
Fatima G. Khushtova
2016-03-01
Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.
Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences
Thabet Abdeljawad
2017-07-01
Full Text Available A discrete version of the symmetric duality of Caputo–Torres, to relate left and right Riemann–Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler–Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.
Structure constants in the N=1 super-Liouville field theory
Poghossian, R.H.
1997-01-01
The symmetry algebra of N=1 super-Liouville field theory in two dimensions is the infinite-dimensional N=1 superconformal algebra, which allows one to prove that correlation functions containing degenerated fields obey some partial linear differential equations. In the special case of four-point function, including a primary field degenerated at the first level, these differential equations can be solved via hypergeometric functions. Taking into account mutual locality properties of fields and investigating s- and t-channel singularities we obtain some functional relations for three-point correlation functions. Solving this functional equations we obtain three-point functions in both Neveu-Schwarz and Ramond sectors. (orig.)
Spectral inversion of an indefinite Sturm-Liouville problem due to Richardson
Shanley, Paul E
2009-01-01
We study an indefinite Sturm-Liouville problem due to Richardson whose complicated eigenvalue dependence on a parameter has been a puzzle for decades. In atomic physics a process exists that inverts the usual Schroedinger situation of an energy eigenvalue depending on a coupling parameter into the so-called Sturmian problem where the coupling parameter becomes the eigenvalue which then depends on the energy. We observe that the Richardson equation is of the Sturmian type. This means that the Richardson and its related Schroedinger eigenvalue functions are inverses of each other and that the Richardson spectrum is therefore no longer a puzzle
On the singular Sturm-Liouville problems that have the same spectrum
Gulsen, Tuba [Department of Mathematics, Firat University, 23119, Elazig (Turkey); Ulusoy, Ismail [Department of Mathematics, Adiyaman University, 02040,Adiyaman (Turkey)
2016-06-08
The problem of efficaciously constucting the potential q (x) and the numbers h and H was solved in [1]. Trubowitz [2] investigated the isospectrality problem which have the same spectrum with other same type of problems. Then Jodeit and Levitan [3] considered this problem with a different approach, based on transmutation operators and integral equation. In this work, we discussed this problem for singular Sturm-Liouville operator and obtained some important formulas for the number H, the potential q (x) and the norming constants α{sub n}.
A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System
Wang, Y.; Xiao, J.
2017-06-01
This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).
Barvik, I [International Centre for Theoretical Physics, Trieste (Italy); Polasek, M [Charles Univ., Prague (Czech Republic). Inst. of Physics; Herman, P [Pedagogical Univ., Hradec Kralove (Czech Republic)
1995-08-01
We used the formal stochastic Liouville equations within Haken-Strobl-Reineker parametrization for the description of the influence of the bath on the memory functions entering the GME for a dimer and a linear trimer with a trap (here modeled as a sink). The often used inclusion of the noncoherent regime in the MF by an exponentially damped prefactor (after Kenkre`s prescription) does not hold for finite systems. The analytical form of the MF is changed more pronouncely and the influence of the sink in the center of the trimer runs parallel with the influence of the bath in destroying the coherence. (author). 60 refs.
Liu, Jian; Zhang, Zhijun
2016-01-01
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems
Dohan, Anthony, E-mail: anthony.dohan@lrb.aphp.fr [Department of Body and Interventional Imaging, Hôpital Lariboisière, AP-HP, 2 Rue Ambroise Paré, 75475 Paris Cedex 10 (France); Université Paris-Diderot, Sorbonne Paris Cité, 10 Rue de Verdun, 75010 Paris (France); UMR INSERM 965, Hôpital Lariboisière, 2 Rue Amboise Paré, 75010 Paris (France); Gavini, Jean-Philippe, E-mail: jpgavini@gmail.com [Department of Body and Interventional Imaging, Hôpital Lariboisière, AP-HP, 2 Rue Ambroise Paré, 75475 Paris Cedex 10 (France); Université Paris-Diderot, Sorbonne Paris Cité, 10 Rue de Verdun, 75010 Paris (France); Placé, Vinciane, E-mail: vinciane.place@gmail.com [Department of Body and Interventional Imaging, Hôpital Lariboisière, AP-HP, 2 Rue Ambroise Paré, 75475 Paris Cedex 10 (France); Sebbag, Delphine, E-mail: delphinesebbag@gmail.com [Department of Body and Interventional Imaging, Hôpital Lariboisière, AP-HP, 2 Rue Ambroise Paré, 75475 Paris Cedex 10 (France); Université Paris-Diderot, Sorbonne Paris Cité, 10 Rue de Verdun, 75010 Paris (France); Vignaud, Alexandre, E-mail: alexandre.vignaud@cea.fr [LRMN, Neurospin, CEA-SACLAY, Bâtiment 145, 91 191 Gif-sur-Yvette Cedex (France); and others
2013-11-01
Objective: To qualitatively and quantitatively compare T2-weighted MR imaging of the liver using volumetric spin-echo with sampling perfection with application-optimized contrast using different flip angle evolutions (SPACE) with conventional turbo spin-echo (TSE) sequence for fat-suppressed T2-weighted MR imaging of the liver. Materials and methods: Thirty-three patients with suspected focal liver lesions had SPACE MR imaging and conventional fat-suppressed TSE MR imaging. Images were analyzed quantitatively by measuring the lesion-to-liver contrast-to-noise ratio (CNR), and the signal-to-noise ratio (SNR) of main focal hepatic lesions, hepatic and splenic parenchyma and qualitatively by evaluating the presence of vascular, respiratory motion and cardiac artifacts. Wilcoxon signed rank test was used to search for differences between the two sequences. Results: SPACE MR imaging showed significantly greater CNR for focal liver lesions (median = 22.82) than TSE MR imaging (median = 14.15) (P < .001). No differences were found for SNR of hepatic parenchyma (P = .097), main focal hepatic lesions (P = .35), and splenic parenchyma (P = .25). SPACE sequence showed less artifacts than TSE sequence (vascular, P < .001; respiratory motion, P < .001; cardiac, P < .001) but needed a longer acquisition time (228.4 vs. 162.1 s; P < .001). Conclusion: SPACE MR imaging provides a significantly increased CNR for focal liver lesions and less artifacts by comparison with the conventional TSE sequence. These results should stimulate further clinical studies with a surgical standard of reference to compare the two techniques in terms of sensitivity for malignant lesions.
Jung, Joon-Yong; Jee, Won-Hee; Park, Michael Y.; Lee, So-Yeon [Seoul St. Mary' s Hospital, The Catholic University of Korea, Department of Radiology, Seoul (Korea, Republic of); Kim, Yang-Soo [Seoul St. Mary' s Hospital, The Catholic University of Korea, Department of Orthopedic Surgery, Seoul (Korea, Republic of)
2012-11-15
To assess the diagnostic performance of shoulder MR arthrography with 3D isotropic fat-suppressed (FS) turbo spin-echo sequence (TSE-SPACE) for supraspinatus tendon tears in comparison with 2D conventional sequences at 3.0 T. The study was HIPAA-compliant and approved by the institutional review board with a waiver of informed consent. Eighty-seven arthroscopically confirmed patients who underwent 3.0 T shoulder MR arthrography with 2D sequences and 3D TSE-SPACE were included in a consecutive fashion from March 2009 to February 2010. Two reviewers independently analyzed 2D sequences and 3D TSE-SPACE. Sensitivity, specificity, accuracy, and interobserver agreement ({kappa}) were compared between 2D sequences and 3D TSE-SPACE for full-thickness and partial-thickness supraspinatus tendon tears together and for partial-thickness supraspinatus tendon tears alone. There were 33 full-thickness tears and 28 partial-thickness tears of supraspinatus tendons. For full-thickness and partial-thickness supraspinatus tendon tears together, the mean sensitivity, specificity, and accuracy of both readers were 96, 92, and 94% on 2D sequences and 91, 84, and 89% on 3D TSE-SPACE. For partial-thickness supraspinatus tendon tears alone, the mean sensitivity, specificity, and accuracy were 95, 92, and 94% on 2D sequences and 84, 85, and 84% on 3D TSE-SPACE. There was no statistical difference between 2D sequences and 3D TSE-SPACE. Interobserver agreements were almost perfect on 2D conventional sequences and substantial on 3D TSE-SPACE. Compared with 2D conventional sequences, MR arthrography using 3D TSE-SPACE was comparable for diagnosing supraspinatus tendon tears despite limitations in detecting small partial-thickness tears and in discriminating between full-thickness and deep partial-thickness tears. (orig.)
Jung, Joon-Yong; Jee, Won-Hee; Park, Michael Y.; Lee, So-Yeon; Kim, Yang-Soo
2012-01-01
To assess the diagnostic performance of shoulder MR arthrography with 3D isotropic fat-suppressed (FS) turbo spin-echo sequence (TSE-SPACE) for supraspinatus tendon tears in comparison with 2D conventional sequences at 3.0 T. The study was HIPAA-compliant and approved by the institutional review board with a waiver of informed consent. Eighty-seven arthroscopically confirmed patients who underwent 3.0 T shoulder MR arthrography with 2D sequences and 3D TSE-SPACE were included in a consecutive fashion from March 2009 to February 2010. Two reviewers independently analyzed 2D sequences and 3D TSE-SPACE. Sensitivity, specificity, accuracy, and interobserver agreement (κ) were compared between 2D sequences and 3D TSE-SPACE for full-thickness and partial-thickness supraspinatus tendon tears together and for partial-thickness supraspinatus tendon tears alone. There were 33 full-thickness tears and 28 partial-thickness tears of supraspinatus tendons. For full-thickness and partial-thickness supraspinatus tendon tears together, the mean sensitivity, specificity, and accuracy of both readers were 96, 92, and 94% on 2D sequences and 91, 84, and 89% on 3D TSE-SPACE. For partial-thickness supraspinatus tendon tears alone, the mean sensitivity, specificity, and accuracy were 95, 92, and 94% on 2D sequences and 84, 85, and 84% on 3D TSE-SPACE. There was no statistical difference between 2D sequences and 3D TSE-SPACE. Interobserver agreements were almost perfect on 2D conventional sequences and substantial on 3D TSE-SPACE. Compared with 2D conventional sequences, MR arthrography using 3D TSE-SPACE was comparable for diagnosing supraspinatus tendon tears despite limitations in detecting small partial-thickness tears and in discriminating between full-thickness and deep partial-thickness tears. (orig.)
Sun Yepeng; Chen Dengyuan
2006-01-01
A new spectral problem and the associated integrable hierarchy of nonlinear evolution equations are presented in this paper. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the hierarchy. Moreover, the corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, new finite-dimensional completely integrable Hamiltonian systems in the Liouville sense. Further, an involutive representation of solution of each equation in the hierarchy is given. Finally, expanding integrable models of the hierarchy are constructed by using a new Loop algebra
Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae
Bleher, P.M.; Kosygin, D.V.; Sinai, Y.G.
1995-01-01
We consider the Weyl asymptotic formula [{E n ≤R 2 }=Area Q.R 2 /(4π)+n(R), for eigenvalues of the Laplace-Beltrami operator on a two-dimensional torus Q with a Liouville metric which is in a sense the most general case of an integrable metric. We prove that if the surface Q is non-degenerate then the remainder term n(R) has the form n(R)=R 1/2 θ(R), where θ(R) is an almost periodic function of the Besicovitch class B 1 , and the Fourier amplitudes and the Fourier frequencies of θ(R) can be expressed via lengths of closed geodesics on Q and other simple geometric characteristics of these geodesics. We prove then that if the surface Q is generic then the limit distribution of θ(R) has a density p(t), which is an entire function of t possessing an asymptotics on a real line, logp(t)∝-C ± t 4 as t→±∞. An explicit expression for the Fourier transform of p(t) via Fourier amplitudes of θ(R) is also given. We obtain the analogue of the Guillemin-Duistermaat trace formula for the Liouville surfaces and discuss its accuracy. (orig.)
Brief comments on Jackiw-Teitelboim gravity coupled to Liouville theory
Giribet, Gaston E
2003-06-07
The Jackiw-Teitelboim gravity with non-vanishing cosmological constant coupled to Liouville theory is considered as a non-critical string on d dimensional flat spacetime. In terms of this interpretation of the model as a consistent string theory, it is discussed as to how the presence of a cosmological constant leads one to consider additional constraints on the parameters of the theory, even though the conformal anomaly is independent of the cosmological constant. The constraints agree with the necessary conditions required to ensure that the tachyon field turns out to be a primary prelogarithmic operator within the context of the worldsheet conformal field theory. Thus, the linearized tachyon field equation allows one to impose the diagonal condition for the interaction term. We analyse the neutralization of the Liouville mode induced by the coupling to the Jackiw-Teitelboim Lagrangian. The standard free field prescription leads one to obtain explicit expressions for three-point functions for the case of vanishing cosmological constant in terms of a product of Shapiro-Virasoro integrals; this fact is a consequence of the mentioned neutralization effect.
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi
2016-01-01
© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-^{1} in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^{L2}(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.
A simple finite element method for boundary value problems with a Riemann–Liouville derivative
Jin, Bangti
2016-02-01
© 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-^{1} in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and ^{L2}(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.
Středa, Pavel; Drchal, Václav
2012-01-01
Roč. 86, č. 19 (2012), "195204-1"-"195204-8" ISSN 1098-0121 R&D Projects: GA ČR(CZ) GAP204/11/1228 Institutional research plan: CEZ:AV0Z10100521; CEZ:AV0Z10100520 Keywords : nonmagnetic semiconductors * spin Hall currents Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.767, year: 2012
Lee, Sungwon; Jee, Won-Hee; Jung, Joon-Yong; Lee, So-Yeon; Ryu, Kyeung-Sik; Ha, Kee-Yong
2015-02-01
Three-dimensional (3D) fast spin-echo sequence with variable flip-angle refocusing pulse allows retrospective alignments of magnetic resonance imaging (MRI) in any desired plane. To compare isotropic 3D T2-weighted (T2W) turbo spin-echo sequence (TSE-SPACE) with standard two-dimensional (2D) T2W TSE imaging for evaluating lumbar spine pathology at 3.0 T MRI. Forty-two patients who had spine surgery for disk herniation and had 3.0 T spine MRI were included in this study. In addition to standard 2D T2W TSE imaging, sagittal 3D T2W TSE-SPACE was obtained to produce multiplanar (MPR) images. Each set of MR images from 3D T2W TSE and 2D TSE-SPACE were independently scored for the degree of lumbar neural foraminal stenosis, central spinal stenosis, and nerve compression by two reviewers. These scores were compared with operative findings and the sensitivities were evaluated by McNemar test. Inter-observer agreements and the correlation with symptoms laterality were assessed with kappa statistics. The 3D T2W TSE and 2D TSE-SPACE had similar sensitivity in detecting foraminal stenosis (78.9% versus 78.9% in 32 foramen levels), spinal stenosis (100% versus 100% in 42 spinal levels), and nerve compression (92.9% versus 81.8% in 59 spinal nerves). The inter-observer agreements (κ = 0.849 vs. 0.451 for foraminal stenosis, κ = 0.809 vs. 0.503 for spinal stenosis, and κ = 0.681 vs. 0.429 for nerve compression) and symptoms correlation (κ = 0.449 vs. κ = 0.242) were better in 3D TSE-SPACE compared to 2D TSE. 3D TSE-SPACE with oblique coronal MPR images demonstrated better inter-observer agreements compared to 3D TSE-SPACE without oblique coronal MPR images (κ = 0.930 vs. κ = 0.681). Isotropic 3D T2W TSE-SPACE at 3.0 T was comparable to 2D T2W TSE for detecting foraminal stenosis, central spinal stenosis, and nerve compression with better inter-observer agreements and symptom correlation. © The Foundation Acta Radiologica 2014 Reprints and
Jung, Joon-Yong; Jee, Won-Hee; Park, Michael Yong [The Catholic University of Korea, Department of Radiology, Seoul St. Mary' s Hospital, College of Medicine, Seoul (Korea, Republic of); Lee, So-Yeon [Sungkyunkwan University School of Medicine, Department of Radiology, Kangbuk Samsung Hospital, Seoul (Korea, Republic of); Kim, Yang-Soo [The Catholic University of Korea, Department of Orthopaedic Surgery, Seoul St. Mary' s Hospital, College of Medicine, Seoul (Korea, Republic of)
2013-02-15
The aim of this study was to determine the accuracy and reliability of shoulder magnetic resonance (MR) arthrography with three-dimensional (3D) isotropic intermediate-weighted turbo spin-echo (TSE) sampling perfection with application-optimised contrasts using different flip angle evolution (SPACE) in the diagnosis of superior labrum anterior-to-posterior (SLAP) lesions compared with two-dimensional (2D) TSE at 3.0 T. MR arthrograms, including 2D TSE and 3D TSE-SPACE, in 87 patients who underwent arthroscopy were retrospectively analysed by two reviewers for the presence and type of SLAP lesions. Sensitivity and specificity were compared using McNemar's test, and inter-observer agreement was calculated using Cohen's kappa. Receiver operating characteristic (ROC) curve analyses were performed. The mean sensitivity, specificity and accuracy were 90%, 85% and 86% for 2D TSE, and 81%, 86% and 85% for 3D TSE-SPACE respectively, with no statistically significant differences. Inter-observer agreements were substantial in 2D TSE ({kappa} = 0.76) and 3D TSE-SPACE ({kappa} = 0.68). The areas under the ROC curves were 0.92 for 2D TSE and 0.90 for 3D TSE-SPACE, which were not significantly different. MR arthrography with 3D TSE-SPACE showed comparable accuracy and substantial inter-observer agreement for the diagnosis of SLAP lesions circle MR arthrography is regarded as the definitive method of shoulder imaging circle Different MR sequences are evolving for SLAP lesions circle 3D TSE-SPACE demonstrated comparable overall accuracy to 2D TSE for SLAP lesions. (orig.)
R. Darzi
2010-01-01
Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
Darzi R; Neamaty A
2010-01-01
We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
Guliyev, Namig J.
2008-01-01
International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.
Bang, J.M.; Gareev, F.A.
1977-01-01
Different convergence properties of the Sturm-Liouville expansion are investigated with particular attention to the case of states which satisfy Schroedinger-like equations with a fixed energy and different depths of a potential, particulary of the Woods-Saxon used in nuclear physics
Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol
2013-01-01
This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.
Valenzuela, Sergio O; Saitoh, Eiji; Kimura, Takashi
2012-01-01
In a new branch of physics and technology called spin-electronics or spintronics, the flow of electrical charge (usual current) as well as the flow of electron spin, the so-called 'spin current', are manipulated and controlled together. This book provides an introduction and guide to the new physics and application of spin current.
Twistor Transform for Spinning Particle
Fedoruk, S.
2005-01-01
Twistorial formulation of a particle of arbitrary spin has been constructed. The twistor formulation is deduced from a space-time formulation of the spinning particle by introducing pure gauge Lorentz harmonics in this system. Canonical transformations and gauge fixing conditions, excluding space-time variables, produce the fundamental conditions of twistor transform relating the space-time formulation and twistor one. Integral transformations, relating massive twistor fields with usual space-time fields, have been constructed
Spinning particle approach to higher spin field theory
Corradini, Olindo
2011-01-01
We shortly review on the connection between higher-spin gauge field theories and supersymmetric spinning particle models. In such approach the higher spin equations of motion are linked to the first-class constraint algebra associated with the quantization of particle models. Here we consider a class of spinning particle models characterized by local O(N)-extended supersymmetry since these models are known to provide an alternative approach to the geometric formulation of higher spin field theory. We describe the canonical quantization of the models in curved target space and discuss the obstructions that appear in presence of an arbitrarily curved background. We then point out the special role that conformally flat spaces appear to have in such models and present a derivation of the higher-spin curvatures for maximally symmetric spaces.
Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
Bourgine, Jean-Emile; Ishiki, Goro; Rim, Chaiho
2012-01-01
We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we investigate the resonance transformation mixing boundary and bulk couplings. It leads to consider two sectors, depending on whether the matter part of the LG correlator is vanishing due to the fusion rules. In the vanishing case, we determine the explicit transformation of the boundary couplings at the first order in bulk couplings. In the non-vanishing case, no bulk-boundary resonance is involved and only the first order of pure boundary resonances have to be considered. Those are encoded in the matrix polynomials determined in our previous paper. We checked the agreement for the bulk-boundary correlators of MM and LG in several non-trivial cases. In this process, we developed an alternative method to derive the boundary resonance encoding polynomials.
A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems
Muhammed I. Syam
2017-11-01
Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.
Riemann-Hilbert treatment of Liouville theory on the torus: the general case
Menotti, Pietro
2011-01-01
We extend the previous treatment of Liouville theory on the torus to the general case in which the distribution of charges is not necessarily symmetric. This requires the concept of Fuchsian differential equation on Riemann surfaces. We show through a group theoretic argument that the Heun parameter and a weight constant are sufficient to satisfy all monodromy conditions. We then apply the technique of differential equations on a Riemann surface to the two-point function on the torus in which one source is arbitrary and the other small. As a byproduct, we give in terms of quadratures the exact Green function on the square and on the rhombus with opening angle 2π/6 in the background of the field generated by an arbitrary charge.
Riemann-Liouville integrals of fractional order and extended KP hierarchy
Kamata, Masaru; Nakamula, Atsushi
2002-01-01
An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators
A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations
Zhang Yufeng; Xu Xixiang
2004-01-01
A subalgebra of loop algebra A-bar 2 is first constructed, which has its own special feature. It follows that a new Liouville integrable hierarchy of evolution equations is obtained, possessing a tri-Hamiltonian structure, which is proved by us in this paper. Especially, three symplectic operators are constructed directly from recurrence relations. The conjugate operator of a recurrence operator is a hereditary symmetry. As reduction cases of the hierarchy presented in this paper, the celebrated MKdV equation and heat-conduction equation are engendered, respectively. Therefore, we call the hierarchy a generalized MKdV-H system. At last, a high-dimension loop algebra G-bar is constructed by making use of a proper scalar transformation. As a result, a type expanding integrable model of the MKdV-H system is given
The Liouville equation for flavour evolution of neutrinos and neutrino wave packets
Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de [Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany)
2016-12-01
We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.
D-branes in N=2 Liouville theory and its mirror
Israel, Dan; Pakman, Ari; Troost, Jan
2005-01-01
We study D-branes in the mirror pair N=2 Liouville/supersymmetric SL(2,R)/U(1) coset superconformal field theories. We build D0-, D1- and D2-branes, on the basis of the boundary state construction for the H 3 + conformal field theory. We also construct D0-branes in an orbifold that rotates the angular direction of the cigar. We show how the poles of correlators associated to localized states and bulk interactions naturally decouple in the one-point functions of localized and extended branes. We stress the role played in the analysis of D-brane spectra by primaries in SL(2,R)/U(1) which are descendents of the parent theory
A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian
Quaas, Alexander; Xia, Aliang
2016-08-01
We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin RN,(-Δ)αv=upin RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.
Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
Shushin, A I
2005-01-01
Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc
Alvarez, Gonzalo A.; Levstein, Patricia R.; Pastawski, Horacio M.
2007-01-01
We have observed an environmentally induced quantum dynamical phase transition in the dynamics of a two-spin experimental swapping gate [G.A. Alvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507]. There, the exchange of the coupled states vertical bar ↑,↓> and vertical bar ↓,↑> gives an oscillation with a Rabi frequency b/ℎ (the spin-spin coupling). The interaction, ℎ/τ SE with a spin-bath degrades the oscillation with a characteristic decoherence time. We showed that the swapping regime is restricted only to bτ SE > or approx. ℎ. However, beyond a critical interaction with the environment the swapping freezes and the system enters to a Quantum Zeno dynamical phase where relaxation decreases as coupling with the environment increases. Here, we solve the quantum dynamics of a two-spin system coupled to a spin-bath within a Liouville-von Neumann quantum master equation and we compare the results with our previous work within the Keldysh formalism. Then, we extend the model to a three interacting spin system where only one is coupled to the environment. Beyond a critical interaction the two spins not coupled to the environment oscillate with the bare Rabi frequency and relax more slowly. This effect is more pronounced when the anisotropy of the system-environment (SE) interaction goes from a purely XY to an Ising interaction form
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut
2014-01-01
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut [School of Medicine, Gazi University, Ankara (Turkey)
2014-12-15
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
CERN. Geneva
2014-01-01
The conjectured relation between higher spin theories on anti de-Sitter (AdS) spaces and weakly coupled conformal field theories is reviewed. I shall then outline the evidence in favour of a concrete duality of this kind, relating a specific higher spin theory on AdS3 to a family of 2d minimal model CFTs. Finally, I shall explain how this relation fits into the framework of the familiar stringy AdS/CFT correspondence.
Konoto, Makoto
2007-01-01
Development of highly effective evaluation technology of magnetic structures on a nanometric scale is a key to understanding spintronics and related phenomena. A high-resolution spin-polarized scanning electron microscope (spin SEM) developed recently is quite suitable for probing such nanostructures because of the capability of analyzing local magnetization vectors in three dimensions. Utilizing the spin SEM, a layered antiferromagnetic structure with the 1nm-alternation of bilayer-sheet magnetization has been successfully resolved. The real-space imaging with full analysis of the temperature-dependent magnetization vectors will be demonstrated. (author)
Peskin, M.E.
1994-01-01
When the strong interactions were a mystery, spin seemed to be just a complication on top of an already puzzling set of phenomena. But now that particle physicists have understood the strong, weak, and electromagnetic interactions, to be gauge theories, with matter built of quarks and leptons, it is recognized that the special properties of spin 1/2 and spin 1 particles have taken central role in the understanding of Nature. The lectures in this summer school will be devoted to the use of spin in unravelling detailed questions about the fundamental interactions. Thus, why not begin by posing a deeper question: Why is there spin? More precisely, why do the basic pointlike constituents of Nature carry intrinsic nonzero quanta of angular momentum? Though the authos has found no definite answer to this question, the pursuit of an answer has led through a wonderful tangle of speculations on the deep structure of Nature. Is spin constructed or is it fundamental? Is it the requirement of symmetry? In the furthest flights taken, it seems that space-time itself is too restrictive a notion, and that this must be generalized in order to gain a full appreciation of spin. In any case, there is no doubt that spin must play a central role in unlocking the mysteries of fundamental physics
Peskin, M.E. [Stanford Univ., CA (United States)
1994-12-01
When the strong interactions were a mystery, spin seemed to be just a complication on top of an already puzzling set of phenomena. But now that particle physicists have understood the strong, weak, and electromagnetic interactions, to be gauge theories, with matter built of quarks and leptons, it is recognized that the special properties of spin 1/2 and spin 1 particles have taken central role in the understanding of Nature. The lectures in this summer school will be devoted to the use of spin in unravelling detailed questions about the fundamental interactions. Thus, why not begin by posing a deeper question: Why is there spin? More precisely, why do the basic pointlike constituents of Nature carry intrinsic nonzero quanta of angular momentum? Though the authos has found no definite answer to this question, the pursuit of an answer has led through a wonderful tangle of speculations on the deep structure of Nature. Is spin constructed or is it fundamental? Is it the requirement of symmetry? In the furthest flights taken, it seems that space-time itself is too restrictive a notion, and that this must be generalized in order to gain a full appreciation of spin. In any case, there is no doubt that spin must play a central role in unlocking the mysteries of fundamental physics.
Spin-polarized light-emitting diodes based on organic bipolar spin valves
Vardeny, Zeev Valentine; Nguyen, Tho Duc; Ehrenfreund, Eitan Avraham
2017-10-25
Spin-polarized organic light-emitting diodes are provided. Such spin-polarized organic light-emitting diodes incorporate ferromagnetic electrodes and show considerable spin-valve magneto-electroluminescence and magneto-conductivity responses, with voltage and temperature dependencies that originate from the bipolar spin-polarized space charge limited current.
Zhao, Li; Chang, Ching-Di; Alsop, David C
2018-02-09
To improve the SNR efficiency and reduce the T 2 blurring of 3D rapid acquisition with relaxation enhancement stack-of-spiral arterial spin labeling imaging by using variable refocusing flip angles and k-space filtering. An algorithm for determining the optimal combination of variable flip angles and filtering correction is proposed. The flip angles are designed using extended phase graph physical simulations in an analytical and global optimization framework, with an optional constraint on deposited power. Optimal designs for correcting to Hann and Fermi window functions were compared with conventional constant amplitude or variable flip angle only designs on 6 volunteers. With the Fermi window correction, the proposed optimal designs provided 39.8 and 27.3% higher SNR (P variable flip angle designs. Even when power deposition was limited to 50% of the constant amplitude design, the proposed method outperformed the SNR (P variable flip angles can be derived as the output of an optimization problem. The combined design of variable flip angle and k-space filtering provided superior SNR to designs primarily emphasizing either approach singly. © 2018 International Society for Magnetic Resonance in Medicine.
Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin
2017-09-01
The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .
Kloth, Jost Karsten, E-mail: jost.kloth@med.uni-heidelberg.de [Diagnostic and Interventional Radiology, University Hospital Heidelberg, Im Neuenheimer Feld 110, D-69120 Heidelberg (Germany); Winterstein, Marianne, E-mail: marianne.winterstein@med.uni-heidelberg.de [Diagnostic and Interventional Radiology, University Hospital Heidelberg, Im Neuenheimer Feld 110, D-69120 Heidelberg (Germany); Akbar, Michael, E-mail: michael.akbar@med.uni-heidelberg.de [Orthopedic and Trauma Surgery, University Hospital Heidelberg, Schlierbacher Landstraße 200a, D-69118 Heidelberg (Germany); Meyer, Esther, E-mail: esther.meyer@siemens.com [Siemens Healthcare, Erlangen (Germany); Paul, Dominik, E-mail: dominik.paul@siemens.com [Siemens Healthcare, Erlangen (Germany); Kauczor, Haus-Ulrich, E-mail: hans-ulrich.kauczor@med.uni-heidelberg.de [Diagnostic and Interventional Radiology, University Hospital Heidelberg, Im Neuenheimer Feld 110, D-69120 Heidelberg (Germany); Weber, Marc-André, E-mail: marcandre.weber@med.uni-heidelberg.de [Diagnostic and Interventional Radiology, University Hospital Heidelberg, Im Neuenheimer Feld 110, D-69120 Heidelberg (Germany)
2014-10-15
Highlights: • 3D SPACE and conventional 2D TSE MRI for assessment of the shoulder joint were compared. • Concordance for most pathologys was substantial to almost perfect. • Examination time could be reduced up to 8 min (27%). • Regarding rotator cuff injuries an additional sagittal T2w TSE sequence in 3D protocol is recommended. - Abstract: Purpose: To determine the accuracy and reliability of three-dimensional (3D) T1- and proton density (PD)-weighted turbo spin-echo (TSE) sampling perfection with application-optimized contrasts using different flip-angle evolution (SPACE) compared with conventional 2D sequences in assessment of the shoulder-joint. Materials and methods: Ninety-three subjects were examined on a 3-T MRI system with both conventional 2D-TSE sequences in T1-, T2- and PD-weighting and 3D SPACE sequences in T1- and PD-weighting. All examinations were assessed independently by two reviewers for common pathologies of the shoulder-joint. Agreement between 2D- and 3D-sequences and inter-observer-agreement was evaluated using kappa-statistics. Results: Using conventional 2D TSE sequences as standard of reference, sensitivity, specificity, and accuracy values of 3D SPACE were 81.8%, 95.1%, and 93.5% for injuries of the supraspinatus-tendon (SSP), 81.3%, 93.5%, and 91.4% for the cartilage layer and 82.4%, 98.5%, and 97.5% for the long biceps tendon. Concordance between 2D and 3D was almost perfect for tendinopathies of the SSP (κ = 0.85), osteoarthritis (κ = 1), luxation of the biceps tendon (κ = 1) and adjacent bone marrow (κ = 0.92). Inter-observer-agreement was generally higher for conventional 2D TSE sequences (κ, 0.23–1.0), when compared to 3D SPACE sequences (κ, −0.33 to 1.0) except for disorders of the long biceps tendon and supraspinatus tendon rupture. Conclusion: Because of substantial and almost perfect concordance with conventional 2D TSE sequences for common shoulder pathologies, MRI examination-time can be reduced by nearly 40
Arkad'ev, V.A.; Pogrebkov, A.K.; Polivanov, M.K.
1988-01-01
The concept of tangent vector is made more precise to meet the specific nature of the Sturm-Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov-Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated
Zhang, G. P., E-mail: gpzhang@indstate.edu [Department of Physics, Indiana State University, Terre Haute, Indiana 47809 (United States); Si, M. S. [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China); George, Thomas F. [Office of the Chancellor and Center for Nanoscience, Departments of Chemistry and Biochemistry and Physics and Astronomy, University of Missouri-St. Louis, St. Louis, Missouri 63121 (United States)
2015-05-07
When a laser pulse excites a ferromagnet, its spin undergoes a dramatic change. The initial demagnetization process is very fast. Experimentally, it is found that the demagnetization time is related to the spin moment in the sample. In this study, we employ the first-principles method to directly simulate such a process. We use the fixed spin moment method to change the spin moment in ferromagnetic nickel, and then we employ the Liouville equation to couple the laser pulse to the system. We find that in general the dependence of demagnetization time on the spin moment is nonlinear: It decreases with the spin moment up to a point, after which an increase with the spin moment is observed, followed by a second decrease. To understand this, we employ an extended Heisenberg model, which includes both the exchange interaction and spin-orbit coupling. The model directly links the demagnetization rate to the spin moment itself and demonstrates analytically that the spin relaxes more slowly with a small spin moment. A future experimental test of our predictions is needed.
Nuclear magnetic relaxation by the dipolar EMOR mechanism: Multi-spin systems
Chang, Zhiwei; Halle, Bertil
2017-08-01
In aqueous systems with immobilized macromolecules, including biological tissues, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. Starting from the stochastic Liouville equation, we have previously developed a rigorous EMOR relaxation theory for dipole-coupled two-spin and three-spin systems. Here, we extend the stochastic Liouville theory to four-spin systems and use these exact results as a guide for constructing an approximate multi-spin theory, valid for spin systems of arbitrary size. This so-called generalized stochastic Redfield equation (GSRE) theory includes the effects of longitudinal-transverse cross-mode relaxation, which gives rise to an inverted step in the relaxation dispersion profile, and coherent spin mode transfer among solid-like spins, which may be regarded as generalized spin diffusion. The GSRE theory is compared to an existing theory, based on the extended Solomon equations, which does not incorporate these phenomena. Relaxation dispersion profiles are computed from the GSRE theory for systems of up to 16 protons, taken from protein crystal structures. These profiles span the range from the motional narrowing limit, where the coherent mode transfer plays a major role, to the ultra-slow motion limit, where the zero-field rate is closely related to the strong-collision limit of the dipolar relaxation rate. Although a quantitative analysis of experimental data is beyond the scope of this work, it is clear from the magnitude of the predicted relaxation rate and the shape of the relaxation dispersion profile that the dipolar EMOR mechanism is the principal cause of water-1H low-field longitudinal relaxation in aqueous systems of immobilized macromolecules, including soft biological tissues. The relaxation theory developed here therefore provides a basis for molecular-level interpretation of endogenous soft
Moura-Melo, W.A.; Pereira, A.R.; Mol, L.A.S.; Pires, A.S.T.
2007-01-01
We study magnetic vortex-like excitations lying on a conic space background. Two types of them are obtained. Their energies appear to be linearly dependent on the conical aperture parameter, besides of being logarithmically divergent with the sample size. In addition, we realize a geometrical-like pinning of the vortex, say, it is energetically favorable for it to nucleate around the conical apex. We also study the problem of two vortices on the cone and obtain an interesting effect on such a geometry: excitations of the same charge, then repealing each other, may nucleate around the apex for suitable cone apertures. We also pay attention to the problem of the vortex pair and how its dissociation temperature depends upon conical geometry
Analysis of geometric phase effects in the quantum-classical Liouville formalism.
Ryabinkin, Ilya G; Hsieh, Chang-Yu; Kapral, Raymond; Izmaylov, Artur F
2014-02-28
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.
Physics-based models for measurement correlations: application to an inverse Sturm–Liouville problem
Bal, Guillaume; Ren Kui
2009-01-01
In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low-frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high-frequency component may significantly affect the measured data. Using simple scaling arguments, we characterize the influence of the high-frequency component. We then consider situations where the correlation function of such an influence may be estimated by asymptotic expansions, for instance as a random corrector in homogenization theory. This allows us to consistently eliminate the high-frequency component and derive a closed form, more accurate, inverse problem for the low-frequency component of the object of interest. We present the asymptotic expression of the correlation matrix of the eigenvalues in a Sturm–Liouville problem with unknown potential. We propose an iterative algorithm for the reconstruction of the potential from knowledge of the eigenvalues and show that using the approximate correlation matrix significantly improves the reconstructions
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Ryabinkin, Ilya G.; Izmaylov, Artur F. [Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada); Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada); Hsieh, Chang-Yu; Kapral, Raymond [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
2014-02-28
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.
Dhar, S.; Basu, B.; Ghosh, Subir
2007-01-01
We explain the intrinsic spin Hall effect from generic anyon dynamics in the presence of external electromagnetic field. The free anyon is represented as a spinning particle with an underlying non-commutative configuration space. The Berry curvature plays a major role in the analysis
Phase space imaging of a beam of charged particles by frictional forces
Daniel, H.
1977-01-01
In the case of frictional forces, defined by always acting opposite to the particle motion, Liouville's theorem does not apply. The effect of such forces on a beam of charged particles is calculated in closed form. Emphasis is given to the phase space imaging by a moderator. Conditions for an increase in phase space density are discussed. (Auth.)
Exact solutions of space-time fractional EW and modified EW equations
Korkmaz, Alper
2017-01-01
The bright soliton solutions and singular solutions are constructed for the space-time fractional EW and the space-time fractional modified EW (MEW) equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform (FCT) and properties of modified Riemann–Liouville derivative. Then, various ansatz method are implemented to construct the solutions for both equations.
Spin transport in spin filtering magnetic tunneling junctions.
Li, Yun; Lee, Eok Kyun
2007-11-01
Taking into account spin-orbit coupling and s-d interaction, we investigate spin transport properties of the magnetic tunneling junctions with spin filtering barrier using Landauer-Büttiker formalism implemented with the recursive algorithm to calculate the real-space Green function. We predict completely different bias dependence of negative tunnel magnetoresistance (TMR) between the systems composed of nonmagnetic electrode (NM)/ferromagnetic barrier (FB)/ferromagnet (FM) and NM/FB/FM/NM spin filtering tunnel junctions (SFTJs). Analyses of the results provide us possible ways of designing the systems which modulate the TMR in the negative magnetoresistance regime.
Valenzuela, Sergio O; Saitoh, Eiji; Kimura, Takashi
2017-01-01
Since the discovery of the giant magnetoresistance effect in magnetic multilayers in 1988, a new branch of physics and technology, called spin-electronics or spintronics, has emerged, where the flow of electrical charge as well as the flow of electron spin, the so-called “spin current,” are manipulated and controlled together. The physics of magnetism and the application of spin current have progressed in tandem with the nanofabrication technology of magnets and the engineering of interfaces and thin films. This book aims to provide an introduction and guide to the new physics and applications of spin current, with an emphasis on the interaction between spin and charge currents in magnetic nanostructures.
Vozková, Markéta
2011-01-01
1 ABSTRACT The aim of this text is to provide an analysis of the phenomenon of spin doctoring in the Euro-Atlantic area. Spin doctors are educated people in the fields of semiotics, cultural studies, public relations, political communication and especially familiar with the infrastructure and the functioning of the media industry. Critical reflection of manipulative communication techniques puts spin phenomenon in historical perspective and traces its practical use in today's social communica...
Bramson, B.D.
1978-01-01
An isolated system in general relativity makes a transition between stationary states. It is shown that the spin vectors of the system, long before and long after the emission of radiation, are supertranslation invariant and, hence, independent of the choice of Minkowski observation space. (author)
Entanglement entropy in random quantum spin-S chains
Saguia, A.; Boechat, B.; Continentino, M. A.; Sarandy, M. S.
2007-01-01
We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin S. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude S of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2 chains using an asymptotically exact real-space renormalization group approach
Conformal description of spinning particles
Todorov, I.T.
1986-01-01
This book is an introduction to the application of the conformal group to quantum field theory of particles with spin. After an introduction to the twistor representations of the conformal group of a conformally flat space-time and twistor flag manifolds with Su(2,2) orbits the classical phase space of conformal spinning particles is described. Thereafter the twistor description of classical zero mass fields is considered together with the quantization. (HSI)
Casanova, David
2012-08-28
The restricted active space spin-flip CI (RASCI-SF) performance is tested in the electronic structure computation of the ground and the lowest electronically excited states in the presence of near-degeneracies. The feasibility of the method is demonstrated by analyzing the avoided crossing between the ionic and neutral singlet states of LiF along the molecular dissociation. The two potential energy surfaces (PESs) are explored by means of the energies of computed adiabatic and approximated diabatic states, dipole moments, and natural orbital electronic occupancies of both states. The RASCI-SF methodology is also used to study the ground and first excited singlet surface crossing involved in the double bond isomerization of ethylene, as a model case. The two-dimensional PESs of the ground (S(0)) and excited (S(1)) states are calculated for the complete configuration space of torsion and pyramidalization molecular distortions. The parameters that define the state energetics in the vicinity of the S(0)/S(1) conical intersection region are compared to complete active space self-consistent field (CASSCF) results. These examples show that it is possible to describe strongly correlated electronic states using a single reference methodology without the need to expand the wavefunction to high levels of collective excitations. Finally, RASCI is also examined in the electronic structure characterization of the ground and 2(1)A(g)(-), 1(1)B(u)(+), 1(1)B(u)(-), and 1(3)B(u)(-) states of all-trans polyenes with two to seven double bonds and beyond. Transition energies are compared to configuration interaction singles, time-dependent density functional theory (TDDFT), CASSCF, and its second-order perturbation correction calculations, and to experimental data. The capability of RASCI-SF to describe the nature and properties of each electronic state is discussed in detail. This example is also used to expose the properties of different truncations of the RASCI wavefunction and to
Korenev, V. L.
2005-01-01
It is shown that spin Hall effect creates uniform spin polarization of electrons in semiconductor with a linear in the momentum spin splitting of conduction band. In turn, the profile of the non-uniform spin polarization accumulated at the edge of the sample oscillates in space even in the absence of an external magnetic field.
Anton, Gisela
1990-01-01
The idea of the intrinsic angular momentum, or 'spin', of a particle has played an essential part in fundamental physics for more than 60 years, and its continuing importance was underlined at the 9th International Symposium on High Energy Spin Physics, held in September in Bonn.
Anton, Gisela
1990-12-15
The idea of the intrinsic angular momentum, or 'spin', of a particle has played an essential part in fundamental physics for more than 60 years, and its continuing importance was underlined at the 9th International Symposium on High Energy Spin Physics, held in September in Bonn.
D' Ariano, G M [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy); Maccone, L [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy); Paini, M [Quantum Optics and Information Group, INFM Udr Pavia, Dipartimento di Fisica ' Alessandro Volta' and INFM, Via Bassi 6, 27100 Pavia (Italy)
2003-02-01
We propose a tomographic reconstruction scheme for spin states. The experimental set-up, which is a modification of the Stern-Gerlach scheme, can be easily performed with currently available technology. The method is generalized to multiparticle states, analysing the spin-1/2 case for indistinguishable particles. Some Monte Carlo numerical simulations are given to illustrate the technique.
D'Ariano, G M; Maccone, L; Paini, M
2003-01-01
We propose a tomographic reconstruction scheme for spin states. The experimental set-up, which is a modification of the Stern-Gerlach scheme, can be easily performed with currently available technology. The method is generalized to multiparticle states, analysing the spin-1/2 case for indistinguishable particles. Some Monte Carlo numerical simulations are given to illustrate the technique
Bovier, Anton
2007-01-01
Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science. This collection of state-of-the-art review papers written by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the mean-field theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models. The book will serve as a concise introduction to the state of the art of spin glass theory, usefull to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Anon.
1989-01-15
The recent 8th International Symposium on High Energy Spin Physics at the University of Minnesota in Minneapolis, Minnesota, opened with a bang when L. Pondrom (Wisconsin), donning a hard hat borrowed from construction workers, ventured that 'spin, the notorious inessential complication of hadronic physics, is finally telling us what real QCD (quantum chromodynamics, the field theory of quarks and gluons) looks like.' He was referring to an animated discussion on the meaning of the recent spin oriented (polarized) scattering results from the European Muon Collaboration (EMC) at CERN and reported at the Symposium by R. Garnet (Liverpool) and P. Schuler (Yale) which show that the proton spin is not simply a reflection of the spins of its constituent quarks.
M.G. Elsheikh
2013-10-01
Full Text Available The unbounded solution, at the points where the boundary conditions change, for a mixed Sturm–Liouville problem of the Dirichlet–Neumann type can be obtained using the method of the integral equation formulation. Since this formulation is usually reduced to an infinite algebraic system in which the unknowns are the Fourier coefficients of the unknown unbounded entity, a study of ℓp-solutions imposes itself concerning the influence of the truncation on such systems. This study is achieved and the well-known theorem on the ℓ2-solutions of the infinite algebraic systems is generalized.
Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar
2018-06-01
In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.
Caspers, W J
1989-01-01
This book is about spin systems as models for magnetic materials, especially antiferromagnetic lattices. Spin-systems are well-defined models, for which, in special cases, exact properties may be derived. These special cases are for the greater part, one- dimensional and restricted in their applicability, but they may give insight into general properties that also exist in higher dimension. This work pays special attention to qualitative differences between spin lattices of different dimensions. It also replaces the traditional picture of an (ordered) antiferromagnetic state of a Heisenberg sy
Gorbachev, D V; Ivanov, V I
2015-01-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles
Buhrman, Robert; Daughton, James; Molnár, Stephan; Roukes, Michael
2004-01-01
This report is a comparative review of spin electronics ("spintronics") research and development activities in the United States, Japan, and Western Europe conducted by a panel of leading U.S. experts in the field. It covers materials, fabrication and characterization of magnetic nanostructures, magnetism and spin control in magnetic nanostructures, magneto-optical properties of semiconductors, and magnetoelectronics and devices. The panel's conclusions are based on a literature review and a series of site visits to leading spin electronics research centers in Japan and Western Europe. The panel found that Japan is clearly the world leader in new material synthesis and characterization; it is also a leader in magneto-optical properties of semiconductor devices. Europe is strong in theory pertaining to spin electronics, including injection device structures such as tunneling devices, and band structure predictions of materials properties, and in development of magnetic semiconductors and semiconductor heterost...
Anon.
1983-01-01
The 5th International Symposium on High Energy Spin Physics met in September at Brookhaven. The symposium has evolved to include a number of diverse specialities: theory, including parity violations and proposed quantum chromodynamics (QCD) tests with polarized beams; experiment, including the large spin effects discovered in high transverse momentum elastic scattering and hyperon production, dibaryons, and magnetic moments; acceleration and storage of polarized protons and electrons; and development of polarized sources and targets
Gelfand-Dickey algebra and higher spin symmetries on T2
Sedra, M.B.
2007-08-01
We focus in this work to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two dimensional torus T 2 . We show in a consistent way, and explicitly, how one can extract these generalized symmetries from the Gelfand-Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed. (author)
Larsen, A.L.; Sanchez, N.
1996-01-01
We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti endash de Sitter spacetimes (as well as in the 2+1 black hole anti endash de Sitter spacetime), all three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti endash de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. copyright 1996 The American Physical Society
Neutron scattering and muon spin rotation as probes of light interstitial transport
Brown, D.W.
1985-01-01
The transport of light interstitials, specifically of hydrogen isotopes and the positive muon, is studied with the help of microscopic transport models. The principal observables are the differential neutron scattering cross section of the hydrogen isotopes and the muon spin rotation signal of the positive muon. The transport feature of primary interest is coherence arising as a result of persistence of quantum mechanical phase memory. Evaluation of observables is based on the generalized master equation, or alternatively, the stochastic Liouville equation. The latter is applied to obtain the neutron scattering lineshapes for local tunneling systems as well as for extended Bravais and non-Bravais lattices. It is found that the usual form of the stochastic Liouville equation does not address adequately transport among non-degenerate site-states. An appropriate modification is suggested and employed to obtain scattering lineshapes applicable to recent experiments on impurity-trapped hydrogen. The muon spin rotation signal is formulated under the assumption that spin interactions constitute a negligible source of scattering for muon transport. The depolarization function is evaluated for the cases of local tunneling systems and simple models of spatially extended transport. The former addresses consequences of coherence and both address the consequences of the spatial extent of the muon wavefunction. It is found that the depolarization function is sensitive to the wave function extent, and the detail attributable to it is characterized
Physical states and BRST operators for higher-spin W strings
Liu, Yu-Xiao; Wei, Shao-Wen; Ren, Ji-Rong; Zhang, Li-Jie
2009-01-01
In this paper, we mainly investigate the W 2,s M x W 2,s L system, in which the matter and the Liouville subsystems generate the W 2,s M and W 2,s L algebras, respectively. We first give a brief discussion of the physical states for the corresponding W strings. The lower states are given by freezing the spin-2 and spin-s currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the W 1,2,s algebras. Based on these linear realizations, the BRST operators for the W 2,s algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the W 2,s L strings at the specific values of the central charges c: c=-(22)/(5) for the W 2,3 L algebra, c=-24 for the W 2,4 L algebra and c=-2,-(286)/(3) for the W 2,6 L algebra, at which the corresponding W 2,s L algebras are singular. (orig.)
Komada, Tomohiro; Naganawa, Shinji; Ogawa, Hiroshi
2008-01-01
We evaluated the newly developed whole-brain, isotropic, 3-dimensional turbo spin-echo imaging with variable flip angle echo train (SPACE) for contrast-enhanced T 1 -weighted imaging in detecting brain metastases at 3 tesla (T). Twenty-two patients with suspected brain metastases underwent postcontrast study with SPACE, magnetization-prepared rapid gradient-echo (MP-RAGE), and 2-dimensional T 1 -weighted spin echo (2D-SE) imaging at 3 T. We quantitatively compared SPACE, MP-RAGE, and 2D-SE images by using signal-to-noise ratios (SNRs) for gray matter (GM) and white matter (WM) and contrast-to-noise ratios (CNRs) for GM-to-WM, lesion-to-GM, and lesion-to-WM. Two blinded radiologists evaluated the detection of brain metastases by segment-by-segment analysis and continuously-distributed test. The CNR between GM and WM was significantly higher on MP-RAGE images than on SPACE images (P 1 -weighted imaging. (author)
On quantum mechanical phase-space wave functions
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....
Open quantum system approach to the modeling of spin recombination reactions.
Tiersch, M; Steiner, U E; Popescu, S; Briegel, H J
2012-04-26
In theories of spin-dependent radical pair reactions, the time evolution of the radical pair, including the effect of the chemical kinetics, is described by a master equation in the Liouville formalism. For the description of the chemical kinetics, a number of possible reaction operators have been formulated in the literature. In this work, we present a framework that allows for a unified description of the various proposed mechanisms and the forms of reaction operators for the spin-selective recombination processes. On the basis of the concept that master equations can be derived from a microscopic description of the spin system interacting with external degrees of freedom, it is possible to gain insight into the underlying microscopic processes and develop a systematic approach toward determining the specific form of the reaction operator in concrete scenarios.
Quantum Mechanics in the Gaussian wave-packet phase space representation: Dynamics
Mizrahi, S.S.
1985-01-01
The Heisenberg and Liouville dynamical equations are mapped using the Wave-Packet Phase Space Representation. A semiclassical perturbative expansion is introduced - the Quasi-Causal Approximation - for the Green function and an expression for transition probabilities is derived up to the first order. (Author) [pt
Extrinsic spin Hall effect in graphene
Rappoport, Tatiana
The intrinsic spin-orbit coupling in graphene is extremely weak, making it a promising spin conductor for spintronic devices. In addition, many applications also require the generation of spin currents in graphene. Theoretical predictions and recent experimental results suggest one can engineer the spin Hall effect in graphene by greatly enhancing the spin-orbit coupling in the vicinity of an impurity. The extrinsic spin Hall effect then results from the spin-dependent skew scattering of electrons by impurities in the presence of spin-orbit interaction. This effect can be used to efficiently convert charge currents into spin-polarized currents. I will discuss recent experimental results on spin Hall effect in graphene decorated with adatoms and metallic cluster and show that a large spin Hall effect can appear due to skew scattering. While this spin-orbit coupling is small if compared with what it is found in metals, the effect is strongly enhanced in the presence of resonant scattering, giving rise to robust spin Hall angles. I will present our single impurity scattering calculations done with exact partial-wave expansions and complement the analysis with numerical results from a novel real-space implementation of the Kubo formalism for tight-binding Hamiltonians. The author acknowledges the Brazilian agencies CNPq, CAPES, FAPERJ and INCT de Nanoestruturas de Carbono for financial support.
Gevorkyan, A.S.; Abajyan, H.G.
2011-01-01
We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The short-range interaction complex-classical Hamiltonian was first used for solving this problem. A system of recurrent equations is obtained on the nodes of the spin-chain lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of the advanced Sylvester conditions which allow step by step construct a huge number of stable spin chains in parallel. The distribution functions of different parameters of spin-glass system are constructed from the first principles of the complex classical mechanics by analyzing the calculation results of the 1D SSCs ensemble. It is shown that the behavior of the parameter distributions is quite different depending on the external fields. The energy ensembles and constants of spin-spin interactions are changed smoothly depending on the external field in the limit of statistical equilibrium, while some of them such as the mean value of polarizations of ensemble and parameters of its orderings are frustrated. We have also studied some critical properties of the ensemble of such catastrophes in the Clausius-Mossotti equation depending on the value of the external field. We have shown that the generalized complex-classical approach excludes these catastrophes allowing one to organize continuous parallel computing on the whole region of values of the external field including critical points. A new representation of the partition function based on these investigations is suggested. As opposed to usual definition, this function is a complex one and its derivatives are everywhere defined, including critical points
Spinning geometry = Twisted geometry
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Manukure, Solomon
2018-04-01
We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.
Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
Gaarde, C.
1985-01-01
An analysis of spectra of (p,n) reactions showed that they were very selective in exciting spin modes. Charge exchange reactions at intermediate energies give important new understanding of the M1-type of excitations and of the spin structure of continuum p spectra in general. In this paper, the author discusses three charge exchange reactions: (p,n); ( 3 H,t); and (d,2p) at several targets. Low-lying states and the Δ region are discussed separately. Finally, the charge exchange reaction with heavy ion beams is briefly discussed. (G.J.P./Auth.)
Beam phase space and emittance
Buon, J.
1992-02-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation, with three particular examples, and to introduce a beam envelope-ellipse and the β-function, emphasing the statistical features of its properties. (author) 14 refs.; 11 figs
Suzuki, T.; Sagawa, H.
2000-01-01
Complete text of publication follows. Spin and isospin modes in nuclei are investigated. We discuss some of the following topics. 1. Spin-dipole excitations in 12 C and 16 O are studied (1). Effects of tensor and spin-orbit interactions on the distribution of the strengths are investigated, and neutral current neutrino scattering cross sections in 16 O are obtained for heavy-flavor neutrinos from the supernovae. 2. Gamow-Teller (GT) and spin-dipole (SD) modes in 208 Bi are investigated. Quenching and fragmentation of the GT strength are discussed (2). SD excitations and electric dipole (E1) transitions between the GT and SD states are studied (3). Calculated E1 strengths are compared with the sum rule values obtained within the 1p-1h and 1p-1h + 2p-2h configuration spaces. 3. Coulomb displacement energy (CDE) of the IAS of 14 Be is calculated, and the effects of the halo on the CDE and the configuration of the halo state are investigated. 4. Spreading width of IAS and isospin dependence of the width are investigated (4). Our formula for the width explains very well the observed isospin dependence (5). (author)
Kovner, Alex
In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. We also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.
Schwarz, H.
2017-01-01
The thesis "Spinning Worlds" is about the characterisation of two types of gas-giant exoplanets: Hot Jupiters, with orbital periods of fewer than five days, and young, wide-orbit gas giants, with orbital periods as long as thousands of years. The thesis is based on near-infrared observations of 1
OPTICS. Quantum spin Hall effect of light.
Bliokh, Konstantin Y; Smirnova, Daria; Nori, Franco
2015-06-26
Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces. Copyright © 2015, American Association for the Advancement of Science.
Spin Hall effect and Berry phase of spinning particles
Berard, Alain; Mohrbach, Herve
2006-01-01
We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non-Abelian Berry gauge connection making the quantum mechanical algebra noncommutative. A generalization to any known spinning particles is possible by using the Bargmann-Wigner equation of motions. The noncommutativity of the coordinates is responsible for the topological spin transport of spinning particles similarly to the spin Hall effect in spintronic physics or the Magnus effect in optics. As an application we predict new dynamics for nonrelativistic particles in an electric field and for photons in a gravitational field
On higher-spin supertranslations and superrotations
Campoleoni, Andrea [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Francia, Dario; Heissenberg, Carlo [Scuola Normale Superiore and INFN,Piazza dei Cavalieri 7, I-56126 Pisa (Italy)
2017-05-22
We study the large gauge transformations of massless higher-spin fields in four-dimensional Minkowski space. Upon imposing suitable fall-off conditions, providing higher-spin counterparts of the Bondi gauge, we observe the existence of an infinite-dimensional asymptotic symmetry algebra. The corresponding Ward identities can be held responsible for Weinberg’s factorisation theorem for amplitudes involving soft particles of spin greater than two.
Relativistic fluid dynamics with spin
Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico
2018-04-01
Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.
Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field
E.A. Ivanchenko
2011-06-01
Full Text Available A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field. The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation. Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.
Covariant form for the conserved currents of the sine-Gordon and Liouville theories
Freedman, D.Z.; Massachusetts Inst. of Tech., Cambridge; Lerda, A.; Massachusetts Inst. of Tech., Cambridge; Penati, S.
1990-01-01
A conserved covariant fourth rank tensor current J μαβγ is constructed for these models both in flat and constant curvature space. For flat space, ∫ dx + J ++++ and its parity conjugate agree with well known results for the lowest grade sine-Gordon conserved charges. However potentially new charges such as ∫ dx + J +++- and ∫ dx + J +++α ε αβ x β either vanish or fail to be conserved because J μαβγ is not symmetric in μ↔γ. There is one curious exception for sine-Gordon models in anti-de Sitter space. (orig.)
Quantum Spin Lenses in Atomic Arrays
A. W. Glaetzle
2017-09-01
Full Text Available We propose and discuss quantum spin lenses, where quantum states of delocalized spin excitations in an atomic medium are focused in space in a coherent quantum process down to (essentially single atoms. These can be employed to create controlled interactions in a quantum light-matter interface, where photonic qubits stored in an atomic ensemble are mapped to a quantum register represented by single atoms. We propose Hamiltonians for quantum spin lenses as inhomogeneous spin models on lattices, which can be realized with Rydberg atoms in 1D, 2D, and 3D, and with strings of trapped ions. We discuss both linear and nonlinear quantum spin lenses: in a nonlinear lens, repulsive spin-spin interactions lead to focusing dynamics conditional to the number of spin excitations. This allows the mapping of quantum superpositions of delocalized spin excitations to superpositions of spatial spin patterns, which can be addressed by light fields and manipulated. Finally, we propose multifocal quantum spin lenses as a way to generate and distribute entanglement between distant atoms in an atomic lattice array.
Spin Coherence in Semiconductor Nanostructures
Flatte, Michael E
2006-01-01
... dots, tuning of spin coherence times for electron spin, tuning of dipolar magnetic fields for nuclear spin, spontaneous spin polarization generation and new designs for spin-based teleportation and spin transistors...
SU (N ) spin-wave theory: Application to spin-orbital Mott insulators
Dong, Zhao-Yang; Wang, Wei; Li, Jian-Xin
2018-05-01
We present the application of the SU (N ) spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders. When taking both spin and orbital degrees of freedom into account rather than projecting Hilbert space onto the Kramers doublet, which is the lowest spin-orbital locked energy levels, the SU (N ) spin-wave theory should take the place of the SU (2 ) one due to the inevitable spin-orbital multipole exchange interactions. To implement the application, we introduce an efficient general local mean-field method, which involves all local fluctuations, and develop the SU (N ) linear spin-wave theory. Our approach is tested firstly by calculating the multipolar spin-wave spectra of the SU (4 ) antiferromagnetic model. Then, we apply it to spin-orbital Mott insulators. It is revealed that the Hund's coupling would influence the effectiveness of the isospin-1 /2 picture when the spin-orbital coupling is not large enough. We further carry out the SU (N ) spin-wave calculations of two materials, α -RuCl3 and Sr2IrO4 , and find that the magnonic and spin-orbital excitations are consistent with experiments.
Higher spin black holes with soft hair
Grumiller, Daniel [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, Vienna, A-1040 (Austria); Pérez, Alfredo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Prohazka, Stefan [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, Vienna, A-1040 (Austria); Tempo, David; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-10-21
We construct a new set of boundary conditions for higher spin gravity, inspired by a recent “soft Heisenberg hair”-proposal for General Relativity on three-dimensional Anti-de Sitter space. The asymptotic symmetry algebra consists of a set of affine û(1) current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin-N, many of which resemble the spin-2 results: the generators of the asymptotic W{sub 3} algebra naturally emerge from composite operators of the û(1) charges through a twisted Sugawara construction; our boundary conditions ensure regularity of the Euclidean solutions space independently of the values of the charges; solutions, which we call “higher spin black flowers”, are stationary but not necessarily spherically symmetric. Finally, we derive the entropy of higher spin black flowers, and find that for the branch that is continuously connected to the BTZ black hole, it depends only on the affine purely gravitational zero modes. Using our map to W-algebra currents we recover well-known expressions for higher spin entropy. We also address higher spin black flowers in the metric formalism and achieve full consistency with previous results.
Mookerjee, Abhijit
1976-01-01
''Spin glasses'', are entire class of magnetic alloys of moderate dilution, in which the magnetic atoms are far enough apart to be unlike the pure metal, but close enough so that the indirect exchange energy between them (mediated by the s-d interaction between local moments and conduction electrons) dominates all other energies. Characteristic critical phenomena displayed such as freezing of spin orientation at 'Tsub(c)' and spreading of magnetic ordering, are pointed out. Anomalous behaviour, associated with these critical phenomena, as reflected in : (i) Moessbauer spectroscopy giving hyperfine splitting at Tsub(c), (ii) maxima in susceptibility and remanent magnetism, (iii) thermopower maxima and change in slope, (iv) Characteristic cusp in susceptibility and its removal by very small magnetic fields, and (v) conductivity-resistivity measurements, are discussed. Theoretical developments aimed at explaining these phenomena, in particular, the ideas from percolation and localisation theories, and the approach based on the gellations of polymers, are discussed. Finally, a new approach based on renormalisation group in disordered systems is also briefly mentioned. (K.B.)
Ohnuma, Yuichi; Matsuo, Mamoru; Maekawa, Sadamichi; Saitoh, Eeiji
2017-01-01
Spin Seebeck and spin Peltier effects, which are mutual conversion phenomena of heat and spin, are discussed on the basis of the microscopic theory. First, the spin Seebeck effect, which is the spin-current generation due to heat current, is discussed. The recent progress in research on the spin Seebeck effect are introduced. We explain the origin of the observed sign changes of the spin Seebeck effect in compensated ferromagnets. Next, the spin Peltier effect, which is the heat-current generation due to spin current, is discussed. Finally, we show that the spin Seebeck and spin Peltier effects are summarized by Onsager's reciprocal relation and derive Kelvin's relation for the spin and heat transports. (author)
Pramanik, S.; bandyopadhyay, S.; Cahay, M.
2003-01-01
We study high-field spin transport of electrons in a quasi one-dimensional channel of a $GaAs$ gate controlled spin interferometer (SPINFET) using a semiclassical formalism (spin density matrix evolution coupled with Boltzmann transport equation). Spin dephasing (or depolarization) is predominantly caused by D'yakonov-Perel' relaxation associated with momentum dependent spin orbit coupling effects that arise due to bulk inversion asymmetry (Dresselhaus spin orbit coupling) and structural inve...
Self-organization of physical fields and spin
Pestov, I.B.
2008-01-01
The subject of the present investigation is the laws of intrinsic self-organization of fundamental physical fields. In the framework of the Theory of Self-Organization the geometrical and physical nature of spin phenomena is uncovered. The key points are spin symmetry (the fundamental realization of the concept of geometrical internal symmetry) and the spinning field (space of defining representation of spin symmetry). It is shown that the essence of spin is the bipolar structure of spin symmetry induced by the gravitational potentials. The bipolar structure provides natural violation of spin symmetry and leads to spinstatics (theory of spinning field outside the time) and spindynamics. The equations of spinstatics and spindynamics are derived. It is shown that Sommerfeld's formula can be derived from the equations of spindynamics and hence the correspondence principle is valid. This means that the Theory of Self-Organization provides the new understanding of spin phenomena
Wirtz, Ludger; Reinhold, Carlos O.; Lemell, Christoph; Burgdoerfer, Joachim
2003-01-01
We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface ('trampoline effect'). For Ne 10+ we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions
Spin tunnelling in mesoscopic systems
Garg, Anupam
2001-02-01
We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.
Spin analysis of supersymmetric particles
Choi, S.Y.; Martyn, H.U.
2006-12-01
The spin of supersymmetric particles can be determined at e + e - colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles -- smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in e + e - collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza-Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an e + e - collider. (orig.)
Magnetic Nanostructures Spin Dynamics and Spin Transport
Farle, Michael
2013-01-01
Nanomagnetism and spintronics is a rapidly expanding and increasingly important field of research with many applications already on the market and many more to be expected in the near future. This field started in the mid-1980s with the discovery of the GMR effect, recently awarded with the Nobel prize to Albert Fert and Peter Grünberg. The present volume covers the most important and most timely aspects of magnetic heterostructures, including spin torque effects, spin injection, spin transport, spin fluctuations, proximity effects, and electrical control of spin valves. The chapters are written by internationally recognized experts in their respective fields and provide an overview of the latest status.
On the quantization of spin systems and Fermi systems
Combe, P.; Rodriguez, R.; Sirugue, M.
1978-03-01
It is shown that spin operators and Fermi operators can be interpreted as the Weyl quantization of some functions on a classical phase space which is a compact group. Moreover the transition from quantum spin to Fermi operators is an isomorphism of the classical phase space preserving the Haar measure
Cao, Xiangyu; Le Doussal, Pierre; Rosso, Alberto; Santachiara, Raoul
2018-04-01
We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.
Spin-polarized spin excitation spectroscopy
Loth, Sebastian; Lutz, Christopher P; Heinrich, Andreas J
2010-01-01
We report on the spin dependence of elastic and inelastic electron tunneling through transition metal atoms. Mn, Fe and Cu atoms were deposited onto a monolayer of Cu 2 N on Cu(100) and individually addressed with the probe tip of a scanning tunneling microscope. Electrons tunneling between the tip and the substrate exchange energy and spin angular momentum with the surface-bound magnetic atoms. The conservation of energy during the tunneling process results in a distinct onset threshold voltage above which the tunneling electrons create spin excitations in the Mn and Fe atoms. Here we show that the additional conservation of spin angular momentum leads to different cross-sections for spin excitations depending on the relative alignment of the surface spin and the spin of the tunneling electron. For this purpose, we developed a technique for measuring the same local spin with a spin-polarized and a non-spin-polarized tip by exchanging the last apex atom of the probe tip between different transition metal atoms. We derive a quantitative model describing the observed excitation cross-sections on the basis of an exchange scattering process.
Spin-dependent optics with metasurfaces
Xiao Shiyi
2016-11-01
Full Text Available Optical spin-Hall effect (OSHE is a spin-dependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components.
Andreev, Pavel A.
2017-02-01
The dielectric permeability tensor for spin polarized plasmas is derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space. Expressions for the distribution function and spin distribution function are derived in linear approximations on the path of dielectric permeability tensor derivation. The dielectric permeability tensor is derived for the spin-polarized degenerate electron gas. It is also discussed at the finite temperature regime, where the equilibrium distribution function is presented by the spin-polarized Fermi-Dirac distribution. Consideration of the spin-polarized equilibrium states opens possibilities for the kinetic modeling of the thermal spin current contribution in the plasma dynamics.
Spin nematics next to spin singlets
Yokoyama, Yuto; Hotta, Chisa
2018-05-01
We provide a route to generate nematic order in a spin-1/2 system. Unlike the well-known magnon-binding mechanism, our spin nematics requires neither the frustration effect nor spin polarization in a high field or in the vicinity of a ferromagnet, but instead appears next to the spin singlet phase. We start from a state consisting of a quantum spin-1/2 singlet dimer placed on each site of a triangular lattice, and show that interdimer ring exchange interactions efficiently dope the SU(2) triplets that itinerate and interact, easily driving a stable singlet state to either Bose-Einstein condensates or a triplet crystal, some hosting a spin nematic order. A variety of roles the ring exchange serves includes the generation of a bilinear-biquadratic interaction between nearby triplets, which is responsible for the emergent nematic order separated from the singlet phase by a first-order transition.
Krejčiřík, David; Siegl, Petr; Železný, Jakub
2014-01-01
Roč. 8, č. 1 (2014), s. 255-281 ISSN 1661-8254 R&D Projects: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701 Grant - others:GA ČR(CZ) GD202/08/H072 Institutional support: RVO:61389005 Keywords : Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert- Schmidt operators Subject RIV: BE - Theoretical Physics Impact factor: 0.545, year: 2014
Prets, A.
1998-07-01
In the present Ph. D. thesis we are considering a special form of scaling limits, namely the hydrodynamic limit. Such limits are considered to explain macroscopic behavior of matter by means of microscopic dynamic laws. In this procedure a rescaling of space and time plays a central role. The limit will be formulated in a quantum mechanical way. Within this framework we study derivations of the Landau Lifshitz equation for ferromagnets. This equation is a macroscopic equation of motion for the magnetization vector and results into the theory of spin waves. Since we have no exact knowledge of the Heisenberg operator's time evolution no definitive statement an how to regain the Landau Lifshitz equation from the microscopic dynamics can be given. In contrast to the Heisenberg operator, for an Ising type interaction inside a ferromagnet one is able to recover macroscopically a solution of a linearized Landau Lifschitz equation. (author)
Proton spin structure in the rest frame
Zavada, P.
1997-01-01
It is shown that the quark-parton model in the standard infinite momentum approach overestimates the proton spin structure function g 1 (x) in comparison with the approach taking consistently into account the internal motion of quarks described by a spherical phase space in the proton rest frame. Particularly, it is shown the first moment of the spin structure function in the latter approach, assuming only the valence quarks contribution to the proton spin, does not contradict the experimental data. copyright 1997 The American Physical Society
Entanglement property in matrix product spin systems
Zhu Jingmin
2012-01-01
We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy S n of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system. (author)
Matsuo, Mamoru; Saitoh, Eiji; Maekawa, Sadamichi
2017-01-01
We investigate the interconversion phenomena between spin and mechanical angular momentum in moving objects. In particular, the recent results on spin manipulation and spin-current generation by mechanical motion are examined. In accelerating systems, spin-dependent gauge fields emerge, which enable the conversion from mechanical angular momentum into spins. Such a spin-mechanical effect is predicted by quantum theory in a non-inertial frame. Experiments which confirm the effect, i.e., the resonance frequency shift in nuclear magnetic resonance, the stray field measurement of rotating metals, and electric voltage generation in liquid metals, are discussed.
Yao Ruo-Xia; Wang Wei; Chen Ting-Hua
2014-01-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)
Max Auwaerter symposium: spin mapping and spin manipulation on the atomic scale
Wiesendanger, R.
2008-01-01
Full text: A fundamental understanding of magnetic and spin-dependent phenomena requires the determination of spin structures and spin excitations down to the atomic scale. The direct visualization of atomic-scale spin structures has first been accomplished for magnetic metals by combining the atomic resolution capability of Scanning Tunnelling Microscopy (STM) with spin sensitivity, based on vacuum tunnelling of spin-polarized electrons. The resulting technique, Spin-Polarized Scanning Tunnelling Microscopy (SP-STM), nowadays provides unprecedented insight into collinear and non-collinear spin structures at surfaces of magnetic nanostructures and has already led to the discovery of new types of magnetic order at the nanoscale. More recently, the development of subkelvin SP-STM has allowed studies of ground-state magnetic properties of individual magnetic adatoms on non-magnetic substrates as well as the magnetic interactions between them. Based on SP-STM experiments performed at temperatures of 300 mK, indirect magnetic exchange interactions at the sub-milli-electronvolt energy scale between individual paramagnetic adatoms as well as between adatoms and nearby magnetic nanostructures could directly be revealed in real space up to distances of several nanometers. In both cases we have observed an oscillatory behavior of the magnetic exchange coupling, alternating between ferromagnetic and antiferromagnetic, as a function of distance. Moreover, the detection of spin-dependent exchange and correlation forces has allowed a first direct real-space observation of spin structures at surfaces of antiferromagnetic insulators. This new type of scanning probe microscopy, called Magnetic Exchange Force Microscopy (MExFM), offers a powerful new tool to investigate different types of spin-spin interactions based on direct-, super-, or RKKY-type exchange down to the atomic level. By combining MExFM with high-precision measurements of damping forces, localized or confined spin
NONE
2006-07-01
The following topics were ealt with: Hadron physics with proton and deuteron probes, physics projects with Georgian participation, spin physics with antiprotons and leptons, spin filtering experiments, ISTC projects, technical issues for FAIR. (HSI)
Dynamic nuclear spin polarization
Stuhrmann, H B [GKSS-Forschungszentrum Geesthacht GmbH (Germany)
1996-11-01
Polarized neutron scattering from dynamic polarized targets has been applied to various hydrogenous materials at different laboratories. In situ structures of macromolecular components have been determined by nuclear spin contrast variation with an unprecedented precision. The experiments of selective nuclear spin depolarisation not only opened a new dimension to structural studies but also revealed phenomena related to propagation of nuclear spin polarization and the interplay of nuclear polarisation with the electronic spin system. The observation of electron spin label dependent nuclear spin polarisation domains by NMR and polarized neutron scattering opens a way to generalize the method of nuclear spin contrast variation and most importantly it avoids precontrasting by specific deuteration. It also likely might tell us more about the mechanism of dynamic nuclear spin polarisation. (author) 4 figs., refs.
Puzynin, I.V.; Puzynina, T.P.; Tkhak, V.Ch.
2010-01-01
SLIPM (Sturm-LIouville Problem in MAPLE) is a program complex written in the language of the computer algebras system MAPLE. It consists of the main program SLIPM.mw and of some procedures. It is intended for a numerical solution with the help of the continuous analog of Newton's method (CANM) of Sturm-Liouville partial problems, i.e. for calculating some eigenvalue of linear second-order differential operator and a corresponding eigenfunction satisfying homogeneous boundary conditions of the general type. SLIPM is the development of the program complexes SLIP1 and SLIPH4 written in the Fortran language. It is added by two new ways of calculating the initial value of iterative parameter τ 0 , by a procedure for calculating a higher precision solution (eigenvalue and corresponding eigenfunction) with the help of Richardson's extrapolation method, by graphical visualization procedures of intermediate and final results of the iterative process and by saving of the results on a disk file. The descriptions of the procedures purposes and their parameters are given
Ji Xiangdong
2003-01-01
Spin is a beautiful concept that plays an ever important role in modern physics. In this talk, I start with a discussion of the origin of spin, and then turn to three themes in which spin has been crucial in subatomic physics: a lab to explore physics beyond the standard model, a tool to measure physical observables that are hard to obtain otherwise, a probe to unravel nonperturbative QCD. I conclude with some remarks on a world without spin
Trembach, Vera
2014-01-01
Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.
Anon.
1980-01-01
From 25 September to 1 October, some 150 spin enthusiasts gathered in Lausanne for the 1980 International Symposium on High Energy Physics with Polarized Beams and Polarized Targets. The programme was densely packed, covering physics interests with spin as well as the accelerator and target techniques which make spin physics possible
Yu, Xiao-Qin; Zhu, Zhen-Gang; Su, Gang
2017-01-01
The thermoelectric performance of a topological energy converter is analyzed. The H-shaped device is based on a combination of transverse topological effects involving the spin: the inverse spin Hall effect and the spin Nernst effect. The device can convert a temperature drop in one arm into an e...
Cross, Rod
2013-01-01
Measurements are presented on the rise of a spinning egg. It was found that the spin, the angular momentum and the kinetic energy all decrease as the egg rises, unlike the case of a ballerina who can increase her spin and kinetic energy by reducing her moment of inertia. The observed effects can be explained, in part, in terms of rolling friction…
Inozemtsev's hyperbolic spin model and its related spin chain
Barba, J.C.; Finkel, F.; Gonzalez-Lopez, A.; Rodriguez, M.A.
2010-01-01
In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.
Coherent spin transport through a 350 micron thick silicon wafer.
Huang, Biqin; Monsma, Douwe J; Appelbaum, Ian
2007-10-26
We use all-electrical methods to inject, transport, and detect spin-polarized electrons vertically through a 350-micron-thick undoped single-crystal silicon wafer. Spin precession measurements in a perpendicular magnetic field at different accelerating electric fields reveal high spin coherence with at least 13pi precession angles. The magnetic-field spacing of precession extrema are used to determine the injector-to-detector electron transit time. These transit time values are associated with output magnetocurrent changes (from in-plane spin-valve measurements), which are proportional to final spin polarization. Fitting the results to a simple exponential spin-decay model yields a conduction electron spin lifetime (T1) lower bound in silicon of over 500 ns at 60 K.
Spin physics in semiconductors
2017-01-01
This book offers an extensive introduction to the extremely rich and intriguing field of spin-related phenomena in semiconductors. In this second edition, all chapters have been updated to include the latest experimental and theoretical research. Furthermore, it covers the entire field: bulk semiconductors, two-dimensional semiconductor structures, quantum dots, optical and electric effects, spin-related effects, electron-nuclei spin interactions, Spin Hall effect, spin torques, etc. Thanks to its self-contained style, the book is ideally suited for graduate students and researchers new to the field.
Flying spin-qubit gates implemented through Dresselhaus and Rashba spin-orbit couplings
Gong, S.J.; Yang, Z.Q.
2007-01-01
A theoretical scheme is proposed to implement flying spin-qubit gates based on two semiconductor wires with Dresselhaus and Rashba spin-orbit couplings (SOCs), respectively. It is found that under the manipulation of the Dresselhaus/Rashba SOC, spin rotates around x/y axis in the three-dimensional spin space. By combining the two kinds of manipulations, i.e. connecting the two kinds of semiconductor wires in series, we obtain a universal set of losses flying single-qubit gates including Hadamard, phase, and π/8 gates. A ballistic switching effect of electronic flow is also found in the investigation. Our results may be useful in future spin or nanoscale electronics
Efficient spin filter using multi-terminal quantum dot with spin-orbit interaction
Yokoyama Tomohiro
2011-01-01
Full Text Available Abstract We propose a multi-terminal spin filter using a quantum dot with spin-orbit interaction. First, we formulate the spin Hall effect (SHE in a quantum dot connected to three leads. We show that the SHE is significantly enhanced by the resonant tunneling if the level spacing in the quantum dot is smaller than the level broadening. We stress that the SHE is tunable by changing the tunnel coupling to the third lead. Next, we perform a numerical simulation for a multi-terminal spin filter using a quantum dot fabricated on semiconductor heterostructures. The spin filter shows an efficiency of more than 50% when the conditions for the enhanced SHE are satisfied. PACS numbers: 72.25.Dc,71.70.Ej,73.63.Kv,85.75.-d
Table for constructing the spin coefficients in general relativity
Cocke, W.J.
1989-01-01
The spin coefficients in spinor calculus in Riemannian space-time are linear functions of the curls of the connecting quantities (the Infeld--Van der Waerden symbols). We show that in the Newman-Penrose formalism the expressions for the spin coefficients are quite manageable, if they are written in terms of the Newman-Penrose tetrad vectors. We present a table of the components of the spin coefficients explicitly in terms of the curls of the individual tetrad vectors
Topological Hall and Spin Hall Effects in Disordered Skyrmionic Textures
N'diaye, P. B.; Akosa, C. A.; Manchon, A.
2016-01-01
We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-B\\"uttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic a...
Inverse spin Hall effect by spin injection
Liu, S. Y.; Horing, Norman J. M.; Lei, X. L.
2007-09-01
Motivated by a recent experiment [S. O. Valenzuela and M. Tinkham, Nature (London) 442, 176 (2006)], the authors present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Their theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering.
Spin-polaron theory of high-Tc superconductivity: I, spin polarons and high-Tc pairing
Wood, R.F.
1993-06-01
The concept of a spin polaron is introduced and contrasted with the more familiar ionic polaron picture. A brief review of aspects of ionic bipolaronic superconductivity is given with particular emphasis on the real-space pairing and true Bose condensation characteristics. The formation energy of spin polarons is then calculated in analogy with ionic polarons. The spin-flip energy of a Cu spin in an antiferromagnetically aligned CuO 2 plane is discussed. It is shown that the introduction of holes into the CuO 2 planes will always lead to the destruction of long-range AF ordering due to the formation of spin polarons. The pairing of two spin polarons can be expected because of the reestablishment of local (short-range) AF ordering; the magnitude of the pairing energy is estimated using a simplified model. The paper closes with a brief discussion of the formal theory of spin polarons
Phase space density representations in fluid dynamics
Ramshaw, J.D.
1989-01-01
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable
Kinetic equation for spin-polarized plasmas
Cowley, S.C.; Kulsrud, R.M.; Valeo, E.
1984-07-01
The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10 -4 S -1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)
Holography and higher-spin theories
Petkou, T.
2005-01-01
I review recent work on the holographic relation between higher-spin theories in Anti-de Sitter spaces and conformal field theories. I present the main results of studies concerning the higher-spin holographic dual of the three-dimensional O(N) vector model. I discuss the special role played by certain double-trace deformations in Conformal Field Theories that have higher-spin holographic duals. Moreover, I show that duality transformations in a U(1) gauge theory on AdS 4 induce boundary double-trace deformations and argue that a similar effect takes place in the holography of linearized higher-spin theories on AdS 4 . (Abstract Copyright [2005], Wiley Periodicals, Inc.)
J-NSE: Neutron spin echo spectrometer
Olaf Holderer
2015-08-01
Full Text Available Neutron Spin-Echo (NSE spectroscopy is well known as the only neutron scattering technique that achieves energy resolution of several neV. By using the spin precession of polarized neutrons in magnetic field one can measure tiny velocity changes of the individual neutron during the scattering process. Contrary to other inelastic neutron scattering techniques, NSE measures the intermediate scattering function S(Q,t in reciprocal space and time directly. The Neutron Spin-Echo spectrometer J-NSE, operated by JCNS, Forschungszentrum Jülich at the Heinz Maier-Leibnitz Zentrum (MLZ in Garching, covers a time range (2 ps to 200 ns on length scales accessible by small angle scattering technique. Along with conventional NSE spectroscopy that allows bulk measurements in transmission mode, J-NSE offers a new possibility - gracing incidence spin echo spectroscopy (GINSENS, developed to be used as "push-button" option in order to resolve the depth dependent near surface dynamics.
Bulk electron spin polarization generated by the spin Hall current
Korenev, V. L.
2005-01-01
It is shown that the spin Hall current generates a non-equilibrium spin polarization in the interior of crystals with reduced symmetry in a way that is drastically different from the previously well-known equilibrium polarization during the spin relaxation process. The steady state spin polarization value does not depend on the strength of spin-orbit interaction offering possibility to generate relatively high spin polarization even in the case of weak spin-orbit coupling.
Bulk electron spin polarization generated by the spin Hall current
Korenev, V. L.
2006-07-01
It is shown that the spin Hall current generates a nonequilibrium spin polarization in the interior of crystals with reduced symmetry in a way that is drastically different from the previously well-known “equilibrium” polarization during the spin relaxation process. The steady state spin polarization value does not depend on the strength of spin-orbit interaction offering possibility to generate relatively high spin polarization even in the case of weak spin-orbit coupling.
Spin with two snakes and overlapping resonances
Lee, S.Y.; Zhao, X.F.
1987-01-01
We study the effect of multiple spin depolarization resonances on the spin of the particles with two snakes. When two resonances are well separated, the polarization can be restored in passing through these resonances provided that the snake resonances are avoided. When two resonances are overlapping, the beam particles may be depolarized depending on the spacing between these two resonances. If the spacing between these two resonances is an odd number for two snakes, the beam particles may be depolarized depending on the strength of the resonance. When the spacing becomes an even number, the spin can tolerate a much larger resonance strength without depolarization. Numerical simulations can be shown to agree well with the analytic formula. However, the spin is susceptible to the combination of an intrinsic and an imperfection resonances even in the presence of the snakes. Numerical simulation indicates that the spin can be restored after the resonances provided that imperfection strength is less than 0.1 if intrinsic strength is fixed at 0.745
Muon spin relaxation in random spin systems
Toshimitsu Yamazaki
1981-01-01
The longitudinal relaxation function Gsub(z)(t) of the positive muon can reflect dynamical characters of local field in a unique way even when the correlation time is longer than the Larmor period of local field. This method has been applied to studies of spin dynamics in spin glass systems, revealing sharp but continuous temperature dependence of the correlation time. Its principle and applications are reviewed. (author)
Slow Manifold and Hannay Angle in the Spinning Top
Berry, M. V.; Shukla, P.
2011-01-01
The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at…
Higher spin gauge theory on fuzzy \\boldsymbol {S^4_N}
Sperling, Marcus; Steinacker, Harold C.
2018-02-01
We examine in detail the higher spin fields which arise on the basic fuzzy sphere S^4N in the semi-classical limit. The space of functions can be identified with functions on classical S 4 taking values in a higher spin algebra associated to \
Maldonado-Velázquez, M. [Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México, 04510 (Mexico); Barrón-Palos, L., E-mail: libertad@fisica.unam.mx [Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 (Mexico); Crawford, C. [University of Kentucky, Lexington, KY 40506 (United States); Snow, W.M. [Indiana University, Bloomington, IN 47405 (United States)
2017-05-11
The neutron spin is a critical degree of freedom for many precision measurements using low-energy neutrons. Fundamental symmetries and interactions can be studied using polarized neutrons. Parity-violation (PV) in the hadronic weak interaction and the search for exotic forces that depend on the relative spin and velocity, are two questions of fundamental physics that can be studied via the neutron spin rotations that arise from the interaction of polarized cold neutrons and unpolarized matter. The Neutron Spin Rotation (NSR) collaboration developed a neutron polarimeter, capable of determining neutron spin rotations of the order of 10{sup −7} rad per meter of traversed material. This paper describes two key components of the NSR apparatus, responsible for the transport and manipulation of the spin of the neutrons before and after the target region, which is surrounded by magnetic shielding and where residual magnetic fields need to be below 100 μG. These magnetic field devices, called input and output coils, provide the magnetic field for adiabatic transport of the neutron spin in the regions outside the magnetic shielding while producing a sharp nonadiabatic transition of the neutron spin when entering/exiting the low-magnetic-field region. In addition, the coils are self contained, forcing the return magnetic flux into a compact region of space to minimize fringe fields outside. The design of the input and output coils is based on the magnetic scalar potential method.
Okuma, Nobuyuki
2017-09-01
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120° structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the z -axis spin rotational symmetry, which can be explained in the context of a singular band point or a U (1 ) symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number Q =-2 , while the typical one observed in topological insulator surface states is characterized by Q =+1 . A magnonic analogue of the surface states, the Dirac magnon with Q =+1 , is found in another kagome lattice antiferromagnet. We also derive the sum rule for Q by using the Poincaré-Hopf index theorem.
Okuma, Nobuyuki
2017-09-08
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120° structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the z-axis spin rotational symmetry, which can be explained in the context of a singular band point or a U(1) symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number Q=-2, while the typical one observed in topological insulator surface states is characterized by Q=+1. A magnonic analogue of the surface states, the Dirac magnon with Q=+1, is found in another kagome lattice antiferromagnet. We also derive the sum rule for Q by using the Poincaré-Hopf index theorem.
Sinova, Jairo; Valenzuela, Sergio O.; Wunderlich, J.; Back, C. H.; Jungwirth, T.
2015-10-01
Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Despite being observed only a decade ago, these effects are already ubiquitous within spintronics, as standard spin-current generators and detectors. Here the theoretical and experimental results that have established this subfield of spintronics are reviewed. The focus is on the results that have converged to give us the current understanding of the phenomena, which has evolved from a qualitative to a more quantitative measurement of spin currents and their associated spin accumulation. Within the experimental framework, optical-, transport-, and magnetization-dynamics-based measurements are reviewed and linked to both phenomenological and microscopic theories of the effect. Within the theoretical framework, the basic mechanisms in both the extrinsic and intrinsic regimes are reviewed, which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. Also reviewed is the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regimes, as well as the spin-pumping theory of spin generation used in many measurements of the spin Hall angle. A further connection to the spin-current-generating spin Hall effect to the inverse spin galvanic effect is given, in which an electrical current induces a nonequilibrium spin polarization. This effect often accompanies the spin Hall effect since they share common microscopic origins. Both can exhibit the same symmetries when present in structures comprising ferromagnetic and nonmagnetic layers through their induced current-driven spin torques or induced voltages. Although a short chronological overview of the evolution of the spin Hall effect field and the resolution of some early controversies is given, the main body of this review is structured from a pedagogical
The susceptibilities in the spin-S Ising model
Ainane, A.; Saber, M.
1995-08-01
The susceptibilities of the spin-S Ising model are evaluated using the effective field theory introduced by Tucker et al. for studying general spin-S Ising model. The susceptibilities are studied for all spin values from S = 1/2 to S = 5/2. (author). 12 refs, 4 figs
Neutron spin quantum precession using multilayer spin splitters and a phase-spin echo interferometer
Ebisawa, Toru; Tasaki, Seiji; Kawai, Takeshi; Hino, Masahiro; Akiyoshi, Tsunekazu; Achiwa, Norio; Otake, Yoshie; Funahashi, Haruhiko.
1996-01-01
Neutron spin quantum precession by multilayer spin splitter has been demonstrated using a new spin interferometer. The multilayer spin splitter consists of a magnetic multilayer mirror on top, followed by a gap layer and a non magnetic multilayer mirror which are evaporated on a silicon substrate. Using the multilayer spin splitter, a polarized neutron wave in a magnetic field perpendicular to the polarization is split into two spin eigenstates with a phase shift in the direction of the magnetic field. The spin quantum precession is equal to the phase shift, which depends on the effective thickness of the gap layer. The demonstration experiments verify the multilayer spin splitter as a neutron spin precession device as well as the coherent superposition principle of the two spin eigenstates. We have developed a new phase-spin echo interferometer using the multilayer spin splitters. We present successful performance tests of the multilayer spin splitter and the phase-spin echo interferometer. (author)
Henneaux, Marc; Vasiliev, Mikhail A
2017-01-01
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...
Korenev, V. L.
2007-01-01
Linearly polarized light tuned slightly below the optical transition of the negatively charged exciton (trion) in a single quantum dot causes the spontaneous nuclear spin polarization (self-polarization) at a level close to 100%. The effective magnetic field of spin-polarized nuclei brings the optical transition energy into resonance with photon energy. The resonantly enhanced Overhauser effect sustains the stability of the nuclear self-polarization even in the absence of spin polarization of...
Nonlinear spin wave coupling in adjacent magnonic crystals
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Spinning-Scroll Pump for Cryogenic Feed System, Phase I
National Aeronautics and Space Administration — The innovation is an efficient, compact, lightweight, reliable, electric-driven, cryogenic spinning scroll pump (CSSP) capable of pumping liquid methane or oxygen at...
The spin and the restrained relativity
Bacry, H.
1992-01-01
The replacement of the Schroedinger position operator by a new one involving the spin variables obliges us to modify slightly the formulas of Lorentz transformations. Here we give a classical description of the way energy, momentum, space and time coordinates transform under a boost. (orig.)
Technologic spin-off from CNEA's activities
Belinco, Cesar G.
2001-01-01
An analysis is made of the spin-off of technology from the nuclear activities in Argentina. Several examples are mentioned in fields such as material sciences, non-destructive testing, forensic research, space activities, instrumentation as well as in environmental studies
Hakioglu, T
2009-01-01
Based on Khodas et al (2004 Phys. Rev. Lett. 92 086602), we propose a device acting like a controllable prism for an incident spin. The device is a large quantum well where Rashba and Dresselhaus spin-orbit interactions are present and controlled by the plunger gate potential, the electric field and the barrier height. A totally destructive interference can be manipulated externally between the Rashba and Dresselhaus couplings. The spin-dependent transmission/reflection amplitudes are calculated as the control parameters are changed. The device operates as a spin prism/converter/filter in different regimes and may stimulate research in promising directions in spintronics in analogy with linear optics.
Bahr, Benjamin; Hellmann, Frank; Kaminski, Wojciech; Kisielowski, Marcin; Lewandowski, Jerzy
2011-01-01
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as our main tool. A set of moves we define in the set of the operator spin foams (among other operations) allows us to split the faces and the edges of the foams. We assign to each operator spin foam a contracted operator, by using the contractions at the vertices and suitably adjusted face amplitudes. The emergence of the face amplitudes is the consequence of assuming the invariance of the contracted operator with respect to the moves. Next, we define spin foam models and consider the class of models assumed to be symmetric with respect to the moves we have introduced, and assuming their partition functions (state sums) are defined by the contracted operators. Briefly speaking, those operator spin foam models are invariant with respect to the cellular decomposition, and are sensitive only to the topology and colouring of the foam. Imposing an extra symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with assumed invariance with respect to the edge splitting move, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on a spin(4) BF spin foam model is exactly the way we tend to view 4D quantum gravity, starting with the BC model and continuing with the Engle-Pereira-Rovelli-Livine (EPRL) or Freidel-Krasnov (FK) models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. Among our natural spin foam models there are the BF spin foam model, the BC model, and a model corresponding to the EPRL intertwiners. Our operator spin foam framework can also be used for more general spin
Dieny, B.; Sousa, R.; Prejbeanu, L.
2007-04-01
Conventional electronics has in the past ignored the spin on the electron, however things began to change in 1988 with the discovery of giant magnetoresistance in metallic thin film stacks which led to the development of a new research area, so called spin-electronics. In the last 10 years, spin-electronics has achieved a number of breakthroughs from the point of view of both basic science and application. Materials research has led to several major discoveries: very large tunnel magnetoresistance effects in tunnel junctions with crystalline barriers due to a new spin-filtering mechanism associated with the spin-dependent symmetry of the electron wave functions new magnetic tunnelling barriers leading to spin-dependent tunnelling barrier heights and acting as spin-filters magnetic semiconductors with increasingly high ordering temperature. New phenomena have been predicted and observed: the possibility of acting on the magnetization of a magnetic nanostructure with a spin-polarized current. This effect, due to a transfer of angular momentum between the spin polarized conduction electrons and the local magnetization, can be viewed as the reciprocal of giant or tunnel magnetoresistance. It can be used to switch the magnetization of a magnetic nanostructure or to generate steady magnetic excitations in the system. the possibility of generating and manipulating spin current without charge current by creating non-equilibrium local accumulation of spin up or spin down electrons. The range of applications of spin electronics materials and phenomena is expanding: the first devices based on giant magnetoresistance were the magnetoresistive read-heads for computer disk drives. These heads, introduced in 1998 with current-in plane spin-valves, have evolved towards low resistance tunnel magnetoresistice heads in 2005. Besides magnetic recording technology, these very sensitive magnetoresistive sensors are finding applications in other areas, in particular in biology. magnetic
Topologically Massive Higher Spin Gravity
Bagchi, A.; Lal, S.; Saha, A.; Sahoo, B.
2011-01-01
We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the
Zeta Function Expression of Spin Partition Functions on Thermal AdS3
Floyd L.Williams
2015-07-01
Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.
Gennes, P.G. de [Commissariat a l' Energie Atomique, Saclay (France)
1959-07-01
The report states an elementary calculation of the correlation between spins in a magnetic substance, and particularly of their asymptotic form with regard to relatively wide-spaced spins. This permits the determination of the phenomenological parameters introduced by Var Hove to describe the magnetic scatter of neutrons in the critical opalescent area. (author) [French] On donne un calcul elementaire des correlations entre spins dans une substance magnetique, et notamment de leur forme asymptotique pour des spins assez eloignes. Ceci permet de determiner les parametres phenomenologiques introduits par Van Hove pour decrire la diffusion magnetique des neutrons dans la region d'opalescence critique. (auteur)
Spin-orbit and spin-lattice coupling
Bauer, Gerrit E.W.; Ziman, Timothy; Mori, Michiyasu
2014-01-01
We pursued theoretical research on the coupling of electron spins in the condensed matter to the lattice as mediated by the spin-orbit interaction with special focus on the spin and anomalous Hall effects. (author)
The spinning minimal surfaces without the Grassmann variables
Barut, A.O.; Pavsic, M.
1988-01-01
Generalizing the model of the spinning Dirac electron with Zitterbewegung we give a theory of spinning strings, membranes and p-branes in curved background spaces of arbitrary dimensions. The dynamical variables are surface co-ordinates x μ (ξ α ) and a single c-number spinor z(ξ α ). We use a phase space action which reduces in the limit to that of spinless membranes. A Hamiltonian formulation is also given. (author). 8 refs
Electrodynamics of spin currents in superconductors
Hirsch, J.E.
2008-01-01
In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the prediction that a spontaneous spin current exists near the surface of superconductors (spin Meissner effect). In this paper we extend the electrodynamic equations proposed earlier for the charge density and charge current to describe also the space and time dependence of the spin density and spin current. This allows us to determine the magnitude of the expelled negative charge and interior electric field as well as of the spin current in terms of other measurable properties of superconductors. We also provide a 'geometric' interpretation of the difference between type I and type II superconductors, discuss how superconductors manage to conserve angular momentum, discuss the relationship between our model and Slater's seminal work on superconductivity, and discuss the magnitude of the expected novel effects for elemental and other superconductors. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Galaxy bispectrum from massive spinning particles
Moradinezhad Dizgah, Azadeh; Lee, Hayden; Muñoz, Julian B.; Dvorkin, Cora
2018-05-01
Massive spinning particles, if present during inflation, lead to a distinctive bispectrum of primordial perturbations, the shape and amplitude of which depend on the masses and spins of the extra particles. This signal, in turn, leaves an imprint in the statistical distribution of galaxies; in particular, as a non-vanishing galaxy bispectrum, which can be used to probe the masses and spins of these particles. In this paper, we present for the first time a new theoretical template for the bispectrum generated by massive spinning particles, valid for a general triangle configuration. We then proceed to perform a Fisher-matrix forecast to assess the potential of two next-generation spectroscopic galaxy surveys, EUCLID and DESI, to constrain the primordial non-Gaussianity sourced by these extra particles. We model the galaxy bispectrum using tree-level perturbation theory, accounting for redshift-space distortions and the Alcock-Paczynski effect, and forecast constraints on the primordial non-Gaussianity parameters marginalizing over all relevant biases and cosmological parameters. Our results suggest that these surveys would potentially be sensitive to any primordial non-Gaussianity with an amplitude larger than fNL≈ 1, for massive particles with spins 2, 3, and 4. Interestingly, if non-Gaussianities are present at that level, these surveys will be able to infer the masses of these spinning particles to within tens of percent. If detected, this would provide a very clear window into the particle content of our Universe during inflation.
Spin Current Noise of the Spin Seebeck Effect and Spin Pumping
Matsuo, M.; Ohnuma, Y.; Kato, T.; Maekawa, S.
2018-01-01
We theoretically investigate the fluctuation of a pure spin current induced by the spin Seebeck effect and spin pumping in a normal-metal-(NM-)ferromagnet(FM) bilayer system. Starting with a simple ferromagnet-insulator-(FI-)NM interface model with both spin-conserving and non-spin-conserving processes, we derive general expressions of the spin current and the spin-current noise at the interface within second-order perturbation of the FI-NM coupling strength, and estimate them for a yttrium-iron-garnet-platinum interface. We show that the spin-current noise can be used to determine the effective spin carried by a magnon modified by the non-spin-conserving process at the interface. In addition, we show that it provides information on the effective spin of a magnon, heating at the interface under spin pumping, and spin Hall angle of the NM.
Spin-1 Dirac-Weyl fermions protected by bipartite symmetry
Lin, Zeren [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); School of Physics, Peking University, Beijing 100871 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)
2015-12-07
We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.
Wigner's infinite spin representations and inert matter
Schroer, Bert [CBPF, Rio de Janeiro (Brazil); Institut fuer Theoretische Physik FU-Berlin, Berlin (Germany)
2017-06-15
Positive energy ray representations of the Poincare group are naturally subdivided into three classes according to their mass and spin content: m > 0, m = 0 finite helicity and m = 0 infinite spin. For a long time the localization properties of the massless infinite spin class remained unknown, until it became clear that such matter does not permit compact spacetime localization and its generating covariant fields are localized on semi-infinite space-like strings. Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this also could happen for finite spin s > 1 fields. This raises the question of a possible connection between inert matter and dark matter. (orig.)
On spin 3 interacting with gravity
Zinoviev, Yu M
2009-01-01
Recently Boulanger and Leclercq have constructed a cubic four derivative 3 - 3 - 2 vertex for the interaction of spin 3 and spin 2 particles. This vertex is trivially invariant under the gauge transformations of the spin 2 field, so it seemed that it could be expressed in terms of the (linearized) Riemann tensor. And indeed in this paper we managed to reproduce this vertex in the form R∂Φ∂Φ, where R is the linearized Riemann tensor and Φ is the completely symmetric third rank tensor. Then we consider the deformation of this vertex to (A)dS space and show that such deformation produces a 'standard' gravitational interaction for spin 3 particles (in the linear approximation) in agreement with general construction of Fradkin and Vasiliev. Then we turn to the massive case and show that the same higher derivative terms allow one to extend the gauge invariant description of a massive spin 3 particle from constant curvature spaces to arbitrary gravitational backgrounds satisfying R μν = 0.
Effect of spin rotation coupling on spin transport
Chowdhury, Debashree; Basu, B.
2013-01-01
We have studied the spin rotation coupling (SRC) as an ingredient to explain different spin-related issues. This special kind of coupling can play the role of a Dresselhaus like coupling in certain conditions. Consequently, one can control the spin splitting, induced by the Dresselhaus like term, which is unusual in a semiconductor heterostructure. Within this framework, we also study the renormalization of the spin-dependent electric field and spin current due to the k → ⋅p → perturbation, by taking into account the interband mixing in the rotating system. In this paper we predict the enhancement of the spin-dependent electric field resulting from the renormalized spin rotation coupling. The renormalization factor of the spin electric field is different from that of the SRC or Zeeman coupling. The effect of renormalized SRC on spin current and Berry curvature is also studied. Interestingly, in the presence of this SRC-induced SOC it is possible to describe spin splitting as well as spin galvanic effect in semiconductors. -- Highlights: •Studied effect of spin rotation coupling on the spin electric field, spin current and Berry curvature. •In the k → ⋅p → framework we study the renormalization of spin electric field and spin current. •For an inertial system we have discussed the spin splitting. •Expression for the Berry phase in the inertial system is discussed. •The inertial spin galvanic effect is studied
Effect of spin rotation coupling on spin transport
Chowdhury, Debashree, E-mail: debashreephys@gmail.com; Basu, B., E-mail: sribbasu@gmail.com
2013-12-15
We have studied the spin rotation coupling (SRC) as an ingredient to explain different spin-related issues. This special kind of coupling can play the role of a Dresselhaus like coupling in certain conditions. Consequently, one can control the spin splitting, induced by the Dresselhaus like term, which is unusual in a semiconductor heterostructure. Within this framework, we also study the renormalization of the spin-dependent electric field and spin current due to the k{sup →}⋅p{sup →} perturbation, by taking into account the interband mixing in the rotating system. In this paper we predict the enhancement of the spin-dependent electric field resulting from the renormalized spin rotation coupling. The renormalization factor of the spin electric field is different from that of the SRC or Zeeman coupling. The effect of renormalized SRC on spin current and Berry curvature is also studied. Interestingly, in the presence of this SRC-induced SOC it is possible to describe spin splitting as well as spin galvanic effect in semiconductors. -- Highlights: •Studied effect of spin rotation coupling on the spin electric field, spin current and Berry curvature. •In the k{sup →}⋅p{sup →} framework we study the renormalization of spin electric field and spin current. •For an inertial system we have discussed the spin splitting. •Expression for the Berry phase in the inertial system is discussed. •The inertial spin galvanic effect is studied.
Spin temperature concept verified by optical magnetometry of nuclear spins
Vladimirova, M.; Cronenberger, S.; Scalbert, D.; Ryzhov, I. I.; Zapasskii, V. S.; Kozlov, G. G.; Lemaître, A.; Kavokin, K. V.
2018-01-01
We develop a method of nonperturbative optical control over adiabatic remagnetization of the nuclear spin system and apply it to verify the spin temperature concept in GaAs microcavities. The nuclear spin system is shown to exactly follow the predictions of the spin temperature theory, despite the quadrupole interaction that was earlier reported to disrupt nuclear spin thermalization. These findings open a way for the deep cooling of nuclear spins in semiconductor structures, with the prospect of realizing nuclear spin-ordered states for high-fidelity spin-photon interfaces.
Spin labels. Applications in biology
Frangopol, T.P.; Frangopol, M.; Ionescu, S.M.; Pop, I.V.; Benga, G.
1980-11-01
The main applications of spin labels in the study of biomembranes, enzymes, nucleic acids, in pharmacology, spin immunoassay are reviewed along with the fundamentals of the spin label method. 137 references. (author)
Spin Switching via Quantum Dot Spin Valves
Gergs, N. M.; Bender, S. A.; Duine, R. A.; Schuricht, D.
2018-01-01
We develop a theory for spin transport and magnetization dynamics in a quantum dot spin valve, i.e., two magnetic reservoirs coupled to a quantum dot. Our theory is able to take into account effects of strong correlations. We demonstrate that, as a result of these strong correlations, the dot gate voltage enables control over the current-induced torques on the magnets and, in particular, enables voltage-controlled magnetic switching. The electrical resistance of the structure can be used to read out the magnetic state. Our model may be realized by a number of experimental systems, including magnetic scanning-tunneling microscope tips and artificial quantum dot systems.
Sung, Jin Kyeong; Jee, Won Hee; Jung, Joon Yong; Jang, Jin Hee; Kim, Jin Sung; Kim, Young Hoon; Ha, Kee Yong [Seoul St. Mary' s Hospital, College of Medicine, The Catholic University of Korea, Seoul (Korea, Republic of)
2017-01-15
To explore the performance of three-dimensional (3D) isotropic T2-weighted turbo spin-echo (TSE) sampling perfection with application optimized contrasts using different flip angle evolution (SPACE) sequence on a 3T system, for the evaluation of nerve root compromise by disc herniation or stenosis from central to extraforaminal location of the lumbar spine, when used alone or in combination with conventional two-dimensional (2D) TSE sequence. Thirty-seven patients who had undergone 3T spine MRI including 2D and 3D sequences, and had subsequent spine surgery for nerve root compromise at a total of 39 nerve levels, were analyzed. A total of 78 nerve roots (48 symptomatic and 30 asymptomatic sites) were graded (0 to 3) using different MRI sets of 2D, 3D (axial plus sagittal), 3D (all planes), and combination of 2D and 3D sequences, with respect to the nerve root compromise caused by posterior disc herniations, lateral recess stenoses, neural foraminal stenoses, or extraforaminal disc herniations; grading was done independently by two readers. Diagnostic performance was compared between different imaging sets using the receiver operating characteristics (ROC) curve analysis. There were no statistically significant differences (p = 0.203 to > 0.999) in the ROC curve area between the imaging sets for both readers 1 and 2, except for combined 2D and 3D (0.843) vs. 2D (0.802) for reader 1 (p = 0.035), and combined 2D and 3D (0.820) vs. 3D including all planes (0.765) for reader 2 (p = 0.049). The performance of 3D isotropic T2-weighted TSE sequence of the lumbar spine, whether axial plus sagittal images, or all planes of images, was not significantly different from that of 2D TSE sequences, for the evaluation of nerve root compromise of the lumbar spine. Combining 2D and 3D might possibly improve the diagnostic accuracy compared with either one.
Hawkes, N
1999-01-01
RAL is fostering commerical exploitation of its research and facilities in two main ways : spin-out companies exploit work done at the lab, spin-in companies work on site taking advantage of the facilities and the expertise available (1/2 page).
Haxton, W.C.
1988-01-01
I discuss a number of the themes of the Symmetries and Spin session of the 8th International Symposium on High Energy Spin Physics: parity nonconservation, CP/T nonconservation, and tests of charge symmetry and charge independence. 28 refs., 1 fig
Classical spins in superconductors
Shiba, H [Tokyo Univ.; Maki, K
1968-08-01
It is shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin. At finite concentration localized excited states around classical spins form an impurity band. The process of growth of the impurity band and its effects on observable quantities are investigated.
Masaike, Akira
1993-01-01
Despite playing a major role in today's Standard Model, spin - the intrinsic angular momentum carried by particles - is sometimes dismissed as an inessential complication. However several major spin questions with important implications for the Standard Model remain unanswered, and recent results and new technological developments made the 10th International Symposium on High Energy Spin Physics, held in Nagoya, Japan, in November, highly topical. The symposium covered a wide range of physics, reflecting the diversity of spin effects, however four main themes were - the spin content of the nucleon, tests of symmetries and physics beyond standard models, intermediate energy physics, and spin technologies. Opening the meeting, T. Kinoshita reviewed the status of measurements of the anomalous magnetic moment (g-2) of the electron and the muon. The forthcoming experiment at Brookhaven (September 1991, page 23) will probe beyond the energy ranges open to existing electronpositron colliders. For example muon substructure will be opened up to 5 TeV and Ws to 2 TeV. R.L. Jaffe classified quark-parton distributions in terms of their spin dependence, pointing out their leftright attributes, and emphasized the importance of measuring transverse spin distributions through lepton pair production
Quantum group spin nets: Refinement limit and relation to spin foams
Dittrich, Bianca; Martin-Benito, Mercedes; Steinhaus, Sebastian
2014-07-01
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so-called "spin nets," for quantum groups SU(2)k and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse-graining procedure, we find a vast nontrivial fixed-point structure beyond the degenerate and the BF phase. In comparison to previous work, we use fixed-point intertwiners, inspired by Reisenberger's construction principle [M. P. Reisenberger, J. Math. Phys. (N.Y.) 40, 2046 (1999)] and the recent work [B. Dittrich and W. Kaminski, arXiv:1311.1798], as the initial parametrization. In this new parametrization fine-tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse-graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.
Jin Lan (兰金
2015-12-01
Full Text Available A diode, a device allowing unidirectional signal transmission, is a fundamental element of logic structures, and it lies at the heart of modern information systems. The spin wave or magnon, representing a collective quasiparticle excitation of the magnetic order in magnetic materials, is a promising candidate for an information carrier for the next-generation energy-saving technologies. Here, we propose a scalable and reprogrammable pure spin-wave logic hardware architecture using domain walls and surface anisotropy stripes as waveguides on a single magnetic wafer. We demonstrate theoretically the design principle of the simplest logic component, a spin-wave diode, utilizing the chiral bound states in a magnetic domain wall with a Dzyaloshinskii-Moriya interaction, and confirm its performance through micromagnetic simulations. Our findings open a new vista for realizing different types of pure spin-wave logic components and finally achieving an energy-efficient and hardware-reprogrammable spin-wave computer.
Lowenstein, D.I.
1985-01-01
Spin Physics at the Alternating Gradient Synchrotron (AGS) of Brookhaven National Laboratory is the most recent of new capabilities being explored at this facility. During the summer of 1984 the AGS accelerated beams of polarized protons to 16.5 GeV/c at 40% polarization to two experiments (E782, E785). These experiments; single spin asymmetry in inclusive polarized pp interactions; and spin-spin effects in polarized pp elastic scattering, operated at the highest polarized proton energy ever achieved by any accelerator in the world. These experiments are reviewed after the complementary spin physics program with unpolarized protons, and the future possibilities with a booster injector for the AGS and the secondary benefits of a Relativisitic Heavy Ion Collider (RHIC), are placed within the context of the present physics program
Superconductivity and spin fluctuations
Scalapino, D.J.
1999-01-01
The organizers of the Memorial Session for Herman Rietschel asked that the author review some of the history of the interplay of superconductivity and spin fluctuations. Initially, Berk and Schrieffer showed how paramagnon spin fluctuations could suppress superconductivity in nearly-ferromagnetic materials. Following this, Rietschel and various co-workers wrote a number of papers in which they investigated the role of spin fluctuations in reducing the Tc of various electron-phonon superconductors. Paramagnon spin fluctuations are also believed to provide the p-wave pairing mechanism responsible for the superfluid phases of 3 He. More recently, antiferromagnetic spin fluctuations have been proposed as the mechanism for d-wave pairing in the heavy-fermion superconductors and in some organic materials as well as possibly the high-Tc cuprates. Here the author will review some of this early history and discuss some of the things he has learned more recently from numerical simulations
Pulsed EPR study of spin coherence time of P donors in isotopically controlled Si
Abe, Eisuke; Isoya, Junichi; Itoh, Kohei M.
2006-01-01
We investigate spin coherence time of electrons bound to phosphorus donors in silicon single crystals. The samples are isotopically controlled so that they may possess various concentrations (from 4.7% to 99.2%) of 29 Si, which is the only non-zero-spin stable isotope of silicon. The orientation dependence of electron-spin coherence times are presented, and electron spin echo envelope modulation is analyzed in time-frequency space
Spin Hall and spin swapping torques in diffusive ferromagnets
Pauyac, C. O.
2017-12-08
A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precessional effects displays a complex spatial dependence that can be exploited to generate torques and nucleate/propagate domain walls in centrosymmetric geometries without use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.
Spin Hall and spin swapping torques in diffusive ferromagnets
Pauyac, C. O.; Chshiev, M.; Manchon, Aurelien; Nikolaev, S. A.
2017-01-01
A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precessional effects displays a complex spatial dependence that can be exploited to generate torques and nucleate/propagate domain walls in centrosymmetric geometries without use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.
Collective effects in spin polarized plasmas
Coppi, B.; Cowley, S.; Detragiache, P.; Kulsrud, R.; Pegoraro, F.
1984-10-01
A fusing plasma with coherently polarized spin nuclei can be subject to instabilities due to the anisotropy of the reaction product distributions in velocity space, which is a result of their polarization. The characteristics of these instabilities depend strongly on the plasma spatial inhomogeneities and a significant rate of spin depolarization can be produced by them if adequate fluctuation amplitudes are reached. The results of the relevant analysis are, in addition, of interest for plasma heating processes with frequencies in the range of the cyclotron frequencies of the considered nuclei
Gravitational instantons in H-spaces
Hacyan, S.
1979-01-01
A spin coefficient method valid for spaces with positive definite metric is presented, together with a Petrov-Penrosetype classification. The theory of H-spaces is applied to self-dual gravitational instantons. (orig.)
Ting, David Z.
2007-01-01
The resonant tunneling spin pump is a proposed semiconductor device that would generate spin-polarized electron currents. The resonant tunneling spin pump would be a purely electrical device in the sense that it would not contain any magnetic material and would not rely on an applied magnetic field. Also, unlike prior sources of spin-polarized electron currents, the proposed device would not depend on a source of circularly polarized light. The proposed semiconductor electron-spin filters would exploit the Rashba effect, which can induce energy splitting in what would otherwise be degenerate quantum states, caused by a spin-orbit interaction in conjunction with a structural-inversion asymmetry in the presence of interfacial electric fields in a semiconductor heterostructure. The magnitude of the energy split is proportional to the electron wave number. Theoretical studies have suggested the possibility of devices in which electron energy states would be split by the Rashba effect and spin-polarized currents would be extracted by resonant quantum-mechanical tunneling.
Nuclear spins in nanostructures
Coish, W.A.; Baugh, J.
2009-01-01
We review recent theoretical and experimental advances toward understanding the effects of nuclear spins in confined nanostructures. These systems, which include quantum dots, defect centers, and molecular magnets, are particularly interesting for their importance in quantum information processing devices, which aim to coherently manipulate single electron spins with high precision. On one hand, interactions between confined electron spins and a nuclear-spin environment provide a decoherence source for the electron, and on the other, a strong effective magnetic field that can be used to execute local coherent rotations. A great deal of effort has been directed toward understanding the details of the relevant decoherence processes and to find new methods to manipulate the coupled electron-nuclear system. A sequence of spectacular new results have provided understanding of spin-bath decoherence, nuclear spin diffusion, and preparation of the nuclear state through dynamic polarization and more general manipulation of the nuclear-spin density matrix through ''state narrowing.'' These results demonstrate the richness of this physical system and promise many new mysteries for the future. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Energy content of stormtime ring current from phase space mapping simulations
Chen, M.W.; Schulz, M.; Lyons, L.R.
1993-01-01
The authors perform a model study to account for the increase in energy content of the trapped-particle population which occurs during the main phase of major geomagnetic storms. They consider stormtime particle transport in the equatorial region of the magnetosphere. They start with a phase space distribution of the ring current before the storm, created by a steady state transport model. They then use a previously developed guiding center particle simulation to map the stormtime ring current phase space, following Liouville's theorem. This model is able to account for the ten to twenty fold increase in energy content of magnetospheric ions during the storm
Consentius, Philipp; Gohlke, Ulrich; Loll, Bernhard; Alings, Claudia; Heinemann, Udo; Wahl, Markus C; Risse, Thomas
2017-08-09
Electron paramagnetic resonance (EPR) spectroscopy in combination with site-directed spin labeling is used to investigate the structure and dynamics of conformationally constrained spin labels in T4 lysozyme single crystals. Within a single crystal, the oriented ensemble of spin bearing moieties results in a strong angle dependence of the EPR spectra. A quantitative description of the EPR spectra requires the determination of the unit cell orientation with respect to the sample tube and the orientation of the spin bearing moieties within the crystal lattice. Angle dependent EPR spectra were analyzed by line shape simulations using the stochastic Liouville equation approach developed by Freed and co-workers and an effective Hamiltonian approach. The gain in spectral information obtained from the EPR spectra of single crystalline samples taken at different frequencies, namely the X-band and Q-band, allows us to discriminate between motional models describing the spectra of isotropic solutions similarly well. In addition, it is shown that the angle dependent single crystal spectra allow us to identify two spin label rotamers with very similar side chain dynamics. These results demonstrate the utility of single crystal EPR spectroscopy in combination with spectral line shape simulation techniques to extract valuable dynamic information not readily available from the analysis of isotropic systems. In addition, it will be shown that the loss of electron density in high resolution diffraction experiments at room temperature does not allow us to conclude that there is significant structural disorder in the system.
Spin drift and spin diffusion currents in semiconductors
Idrish Miah, M [Nanoscale Science and Technology Centre and School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111 (Australia)], E-mail: m.miah@griffith.edu.au
2008-09-15
On the basis of a spin drift-diffusion model, we show how the spin current is composed and find that spin drift and spin diffusion contribute additively to the spin current, where the spin diffusion current decreases with electric field while the spin drift current increases, demonstrating that the extension of the spin diffusion length by a strong field does not result in a significant increase in spin current in semiconductors owing to the competing effect of the electric field on diffusion. We also find that there is a spin drift-diffusion crossover field for a process in which the drift and diffusion contribute equally to the spin current, which suggests a possible method of identifying whether the process for a given electric field is in the spin drift or spin diffusion regime. Spin drift-diffusion crossover fields for GaAs are calculated and are found to be quite small. We derive the relations between intrinsic spin diffusion length and the spin drift-diffusion crossover field of a semiconductor for different electron statistical regimes. The findings resulting from this investigation might be important for semiconductor spintronics.
Spin drift and spin diffusion currents in semiconductors
M Idrish Miah
2008-01-01
Full Text Available On the basis of a spin drift-diffusion model, we show how the spin current is composed and find that spin drift and spin diffusion contribute additively to the spin current, where the spin diffusion current decreases with electric field while the spin drift current increases, demonstrating that the extension of the spin diffusion length by a strong field does not result in a significant increase in spin current in semiconductors owing to the competing effect of the electric field on diffusion. We also find that there is a spin drift-diffusion crossover field for a process in which the drift and diffusion contribute equally to the spin current, which suggests a possible method of identifying whether the process for a given electric field is in the spin drift or spin diffusion regime. Spin drift-diffusion crossover fields for GaAs are calculated and are found to be quite small. We derive the relations between intrinsic spin diffusion length and the spin drift-diffusion crossover field of a semiconductor for different electron statistical regimes. The findings resulting from this investigation might be important for semiconductor spintronics.
Spin drift and spin diffusion currents in semiconductors
Idrish Miah, M
2008-01-01
On the basis of a spin drift-diffusion model, we show how the spin current is composed and find that spin drift and spin diffusion contribute additively to the spin current, where the spin diffusion current decreases with electric field while the spin drift current increases, demonstrating that the extension of the spin diffusion length by a strong field does not result in a significant increase in spin current in semiconductors owing to the competing effect of the electric field on diffusion. We also find that there is a spin drift-diffusion crossover field for a process in which the drift and diffusion contribute equally to the spin current, which suggests a possible method of identifying whether the process for a given electric field is in the spin drift or spin diffusion regime. Spin drift-diffusion crossover fields for GaAs are calculated and are found to be quite small. We derive the relations between intrinsic spin diffusion length and the spin drift-diffusion crossover field of a semiconductor for different electron statistical regimes. The findings resulting from this investigation might be important for semiconductor spintronics.
Quantifying Spin Hall Angles from Spin Pumping : Experiments and Theory
Mosendz, O.; Pearson, J.E.; Fradin, F.Y.; Bauer, G.E.W.; Bader, S.D.; Hoffmann, A.
2010-01-01
Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating Ni80Fe20|normal metal (N) bilayers into a coplanar
Compound nucleus effects in spin-spin cross sections
Thompson, W.J.
1976-01-01
By comparison with recent data, it is shown that spin-spin cross sections for low-energy neutrons may be dominated by a simple compound-elastic level-density effect, independent of spin-spin terms in the nucleon-nucleus optical-model potential. (Auth.)
Strain-induced large spin splitting and persistent spin helix at LaAlO$_3$/SrTiO$_3$ interface
Yamaguchi, Naoya; Ishii, Fumiyuki
2017-01-01
We investigated the effect of the tensile strain on the spin splitting at the n-type interface in LaAlO$_3$/SrTiO$_3$ in terms of the spin-orbit coupling coefficient $\\alpha$ and spin texture in the momentum space using first-principles calculations. We found that the $\\alpha$ could be controlled by the tensile strain and be enhanced up to 5 times for the tensile strain of 7%, and the effect of the tensile strain leads to a persistent spin helix, which has a long spin lifetime. These results ...
2013-01-01
This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can - within a single book - obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated
SPINning parallel systems software
Matlin, O.S.; Lusk, E.; McCune, W.
2002-01-01
We describe our experiences in using Spin to verify parts of the Multi Purpose Daemon (MPD) parallel process management system. MPD is a distributed collection of processes connected by Unix network sockets. MPD is dynamic processes and connections among them are created and destroyed as MPD is initialized, runs user processes, recovers from faults, and terminates. This dynamic nature is easily expressible in the Spin/Promela framework but poses performance and scalability challenges. We present here the results of expressing some of the parallel algorithms of MPD and executing both simulation and verification runs with Spin
McWeeny, Roy
2004-01-01
Originally delivered as a series of lectures, this volume systematically traces the evolution of the ""spin"" concept from its role in quantum mechanics to its assimilation into the field of chemistry. Author Roy McWeeny presents an in-depth illustration of the deductive methods of quantum theory and their application to spins in chemistry, following the path from the earliest concepts to the sophisticated physical methods employed in the investigation of molecular structure and properties. Starting with the origin and development of the spin concept, the text advances to an examination of sp
NUCLEON SPIN: Enigma confirmed
Anon.
1994-01-01
In 1987 the European Muon Collaboration (EMC - June 1988, page 9) reported results from a polarized muon-proton scattering experiment at CERN which puzzled the particle and nuclear physics communities. Contrary to the prediction of the naive quark model, the EMC found that little of the proton spin seemed to be carried by the spins of the quarks. An extensive experimental programme was therefore immediately proposed at CERN, SLAC (Stanford) and DESY (Hamburg) to measure the spin structure function of the neutron and to repeat the proton measurement with improved accuracy
Khan, H.
1990-01-01
This thesis explores deep inelastic scattering of a lepton beam from a polarized nuclear target with spin J=1. After reviewing the formation for spin-1/2, the structure functions for a spin-1 target are defined in terms of the helicity amplitudes for forward compton scattering. A version of the convolution model, which incorporates relativistic and binding energy corrections is used to calculate the structure functions of a neutron target. A simple parameterization of these structure functions is given in terms of a few neutron wave function parameters and the free nucleon structure functions. This allows for an easy comparison of structure functions calculated using different neutron models. (author)
Wunderlich, Joerg; Park, B.G.; Irvine, A.C.; Zarbo, Liviu; Rozkotová, E.; Němec, P.; Novák, Vít; Sinova, Jairo; Jungwirth, Tomáš
2010-01-01
Roč. 330, č. 6012 (2010), s. 1801-1804 ISSN 0036-8075 R&D Projects: GA AV ČR KAN400100652; GA MŠk LC510 EU Projects: European Commission(XE) 215368 - SemiSpinNet Grant - others:AV ČR(CZ) AP0801 Program:Akademická prémie - Praemium Academiae Institutional research plan: CEZ:AV0Z10100521 Keywords : spin Hall effect * spintronics * spin transistor Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 31.364, year: 2010
Chang Wenkua; Zheng Han
1989-01-01
The effects of spinning process parameters including max. pass percentage reduction, spinning temperature, feed rate, lubricant and annealing technology on the quality of shaped components are summarized and discussed in the present paper. The above mentioned parameters are adopted in the process of spinning of barrel-shaped and specially shaped components of refractory metals and their alloys W, Mo, Nb, Zr, TZM molybdenum alloy, C-103, C-752 niobium alloy etc. The cause of leading to usual defects of spun products of refractory metals such as lamellar as 'scaling', crack, swelling, wrinkle, etc. have been analysed and the ways to eliminate the defects have been put forward. 8 figs., 5 tabs. (Author)
Self-interacting spin-2 dark matter
Chu, Xiaoyong; Garcia-Cely, Camilo
2017-11-01
Recent developments in bigravity allow one to construct consistent theories of interacting spin-2 particles that are free of ghosts. In this framework, we propose an elementary spin-2 dark matter candidate with a mass well below the TeV scale. We show that, in a certain regime where the interactions induced by the spin-2 fields do not lead to large departures from the predictions of general relativity, such a light dark matter particle typically self-interacts and undergoes self-annihilations via 3-to-2 processes. We discuss its production mechanisms and also identify the regions of the parameter space where self-interactions can alleviate the discrepancies at small scales between the predictions of the collisionless dark matter paradigm and cosmological N-body simulations.
Spin transfer torque with spin diffusion in magnetic tunnel junctions
Manchon, Aurelien
2012-08-09
Spin transport in magnetic tunnel junctions in the presence of spin diffusion is considered theoretically. Combining ballistic tunneling across the barrier and diffusive transport in the electrodes, we solve the spin dynamics equation in the metallic layers. We show that spin diffusion mixes the transverse spin current components and dramatically modifies the bias dependence of the effective spin transfer torque. This leads to a significant linear bias dependence of the out-of-plane torque, as well as a nonconventional thickness dependence of both spin torque components.
Electron spin and nuclear spin manipulation in semiconductor nanosystems
Hirayama, Yoshiro; Yusa, Go; Sasaki, Satoshi
2006-01-01
Manipulations of electron spin and nuclear spin have been studied in AlGaAs/GaAs semiconductor nanosystems. Non-local manipulation of electron spins has been realized by using the correlation effect between localized and mobile electron spins in a quantum dot- quantum wire coupled system. Interaction between electron and nuclear spins was exploited to achieve a coherent control of nuclear spins in a semiconductor point contact device. Using this device, we have demonstrated a fully coherent manipulation of any two states among the four spin levels of Ga and As nuclei. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Tensor algebra over Hilbert space: Field theory in classical phase space
Matos Neto, A.; Vianna, J.D.M.
1984-01-01
It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt
When measured spin polarization is not spin polarization
Dowben, P A; Wu Ning; Binek, Christian
2011-01-01
Spin polarization is an unusually ambiguous scientific idiom and, as such, is rarely well defined. A given experimental methodology may allow one to quantify a spin polarization but only in its particular context. As one might expect, these ambiguities sometimes give rise to inappropriate interpretations when comparing the spin polarizations determined through different methods. The spin polarization of CrO 2 and Cr 2 O 3 illustrate some of the complications which hinders comparisons of spin polarization values. (viewpoint)
Spin-4 extended conformal algebras
Kakas, A.C.
1988-01-01
We construct spin-4 extended conformal algebras using the second hamiltonian structure of the KdV hierarchy. In the presence of a U(1) current a family of spin-4 algebras exists but the additional requirement that the spin-1 and spin-4 currents commute fixes the algebra uniquely. (orig.)
Anisotropic spin relaxation in graphene
Tombros, N.; Tanabe, S.; Veligura, A.; Jozsa, C.; Popinciuc, M.; Jonkman, H. T.; van Wees, B. J.
2008-01-01
Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular
Spin squeezing and quantum correlations
2 states. A coherent spin-s state. (CSS) θ φ can then be thought of as having no quantum correlations as the constituent. 2s elementary spins point in the same direction ˆn(θ φ) which is the mean spin direction. 2. State classification and squeezing. In order to discuss squeezing, we begin with the squeezing condition itself.
O'FAllon, J.R.
1991-01-01
The history of spin physics experiments is presented, with emphasis of Kent Terwilliger's involvement. Development of polarized beams and targets at the ZGS and AGS is recalled. P-P elastic scattering experiments are reviewed
Ratcliffe, P.G.
1993-01-01
A discussion is presented of the role that transverse spin physics can play in providing information on the bound state dynamics in hadronic physics. Care is taken to distinguish between single- and double-spin measurements, each being discussed separately. In the case of single-spin effects it is stressed that as yet no satisfactory explanation has been provided within the framework if perturbative QCD which in fact generally predicts negligible effects. In order to clarify the situation experimental data at yet higher p T are necessary and semi-leptonic data could shed some light on the underlying scattering mechanisms. As regards double-spin correlations, the theoretical picture (although clouded by some ill-informed, often erroneous statements and even recent papers) is rather well understood and what is dearly missing is the experimental study of, for example, g 2 in deep-inelastic scattering. (author). 31 refs
Glyde, H.R.; Hernadi, S.I.
1986-01-01
Several ground state properties of (electron) spin-polarized deuterium (D) such as the energy, single quasiparticle energies and lifetimes, Landau parameters and sound velocities are evaluated. The calculations begin with the Kolos-Wolneiwicz potential and use the Galitskii-FeynmanHartree-Fock (GFHF) approximation. The deuteron nucleas has spin I = 1, and spin states I/sub z/ = 1,0,-1. We explore D 1 , D 2 and D 3 in which, respectively, one spin state only is populated, two states are equally populated, and three states are equally populated. We find the GFHF describes D 1 well, but D 2 and D 3 less well. The Landau parameters, F/sub L/, are small compared to liquid 3 He and very small for doubly polarized D 1 (i.e. the F/sub L/ decrease with nuclear polarization)
Microscopic studies of nonlocal spin dynamics and spin transport (invited)
Adur, Rohan; Du, Chunhui; Cardellino, Jeremy; Scozzaro, Nicolas; Wolfe, Christopher S.; Wang, Hailong; Herman, Michael; Bhallamudi, Vidya P.; Pelekhov, Denis V.; Yang, Fengyuan; Hammel, P. Chris, E-mail: hammel@physics.osu.edu [Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)
2015-05-07
Understanding the behavior of spins coupling across interfaces in the study of spin current generation and transport is a fundamental challenge that is important for spintronics applications. The transfer of spin angular momentum from a ferromagnet into an adjacent normal material as a consequence of the precession of the magnetization of the ferromagnet is a process known as spin pumping. We find that, in certain circumstances, the insertion of an intervening normal metal can enhance spin pumping between an excited ferromagnetic magnetization and a normal metal layer as a consequence of improved spin conductance matching. We have studied this using inverse spin Hall effect and enhanced damping measurements. Scanned probe magnetic resonance techniques are a complementary tool in this context offering high resolution magnetic resonance imaging, localized spin excitation, and direct measurement of spin lifetimes or damping. Localized magnetic resonance studies of size-dependent spin dynamics in the absence of lithographic confinement in both ferromagnets and paramagnets reveal the close relationship between spin transport and spin lifetime at microscopic length scales. Finally, detection of ferromagnetic resonance of a ferromagnetic film using the photoluminescence of nitrogen vacancy spins in neighboring nanodiamonds demonstrates long-range spin transport between insulating materials, indicating the complexity and generality of spin transport in diverse, spatially separated, material systems.
Microscopic studies of nonlocal spin dynamics and spin transport (invited)
Adur, Rohan; Du, Chunhui; Cardellino, Jeremy; Scozzaro, Nicolas; Wolfe, Christopher S.; Wang, Hailong; Herman, Michael; Bhallamudi, Vidya P.; Pelekhov, Denis V.; Yang, Fengyuan; Hammel, P. Chris
2015-05-01
Understanding the behavior of spins coupling across interfaces in the study of spin current generation and transport is a fundamental challenge that is important for spintronics applications. The transfer of spin angular momentum from a ferromagnet into an adjacent normal material as a consequence of the precession of the magnetization of the ferromagnet is a process known as spin pumping. We find that, in certain circumstances, the insertion of an intervening normal metal can enhance spin pumping between an excited ferromagnetic magnetization and a normal metal layer as a consequence of improved spin conductance matching. We have studied this using inverse spin Hall effect and enhanced damping measurements. Scanned probe magnetic resonance techniques are a complementary tool in this context offering high resolution magnetic resonance imaging, localized spin excitation, and direct measurement of spin lifetimes or damping. Localized magnetic resonance studies of size-dependent spin dynamics in the absence of lithographic confinement in both ferromagnets and paramagnets reveal the close relationship between spin transport and spin lifetime at microscopic length scales. Finally, detection of ferromagnetic resonance of a ferromagnetic film using the photoluminescence of nitrogen vacancy spins in neighboring nanodiamonds demonstrates long-range spin transport between insulating materials, indicating the complexity and generality of spin transport in diverse, spatially separated, material systems.
Microscopic studies of nonlocal spin dynamics and spin transport (invited)
Adur, Rohan; Du, Chunhui; Cardellino, Jeremy; Scozzaro, Nicolas; Wolfe, Christopher S.; Wang, Hailong; Herman, Michael; Bhallamudi, Vidya P.; Pelekhov, Denis V.; Yang, Fengyuan; Hammel, P. Chris
2015-01-01
Understanding the behavior of spins coupling across interfaces in the study of spin current generation and transport is a fundamental challenge that is important for spintronics applications. The transfer of spin angular momentum from a ferromagnet into an adjacent normal material as a consequence of the precession of the magnetization of the ferromagnet is a process known as spin pumping. We find that, in certain circumstances, the insertion of an intervening normal metal can enhance spin pumping between an excited ferromagnetic magnetization and a normal metal layer as a consequence of improved spin conductance matching. We have studied this using inverse spin Hall effect and enhanced damping measurements. Scanned probe magnetic resonance techniques are a complementary tool in this context offering high resolution magnetic resonance imaging, localized spin excitation, and direct measurement of spin lifetimes or damping. Localized magnetic resonance studies of size-dependent spin dynamics in the absence of lithographic confinement in both ferromagnets and paramagnets reveal the close relationship between spin transport and spin lifetime at microscopic length scales. Finally, detection of ferromagnetic resonance of a ferromagnetic film using the photoluminescence of nitrogen vacancy spins in neighboring nanodiamonds demonstrates long-range spin transport between insulating materials, indicating the complexity and generality of spin transport in diverse, spatially separated, material systems
Nucleon Spin Structure: Longitudinal and Transverse
Chen, Jian-Ping
2011-01-01
Inclusive Deep-Inelastic Scattering (DIS) experiments have provided us with the most extensive information on the unpolarized and longitudinal polarized parton (quark and gluon) distributions in the nucleon. It has becoming clear that transverse spin and transverse momentum dependent distributions (TMDs) study are crucial for a more complete understanding of the nucleon structure and the dynamics of the strong interaction. The transverse spin structure and the TMDs are the subject of increasingly intense theoretical and experimental study recently. With a high luminosity electron beam facility, JLab has played a major role in the worldwide effort to study both the longitudinal and transverse spin structure. Highlights of recent results will be presented. With 12-GeV energy upgrade, JLab will provide the most precise measurements in the valence quark region to close a chapter in longitudinal spin study. JLab will also perform a multi-dimensional mapping of the transverse spin structure and TMDs in the valence quark region through Semi-Inclusive DIS (SIDIS) experiments, providing a 3-d partonic picture of the nucleon in momentum space and extracting the u and d quark tensor charges of the nucleon. The precision mapping of TMDs will also allow a detailed study of the quark orbital motion and its dynamics.
Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.
Liang, Zhichun; Crepeau, Richard H; Freed, Jack H
2005-12-01
Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.
Exertional Rhabdomyolysis after Spinning
Jeong, Youjin; Kweon, Hyuk-Jung; Oh, Eun-Jung; Ahn, Ah-Leum; Choi, Jae-Kyung; Cho, Dong-Yung
2016-01-01
Any strenuous muscular exercise may trigger rhabdomyolysis. We report an episode of clinically manifested exertional rhabdomyolysis due to stationary cycling, commonly known as spinning. Reports of spinning-related rhabdomyolysis are rare in the English literature, and the current case appears to be the first such case reported in South Korea. A previously healthy 21-year-old Asian woman presented with severe thigh pain and reddish-brown urinary discoloration 24?48 hours after attending a spi...
Modeling Spin Creation and Mass Generation in the Electron Motivated by an Angle Doubler Mechanism
2017-11-01
that the very high frequency Zitterbewegung oscillations in internal space cannot be followed in lock -step by physical space. Figure 10 shows a...cannot be followed in lock step and a lag exists in physical space with respect to internal space. The lag drags physical space generating both spin...Perhaps this question can be answered if we relax the separate identities of internal space and physical space. Consider that physical space for a photon
Salberger, Olof; Korepin, Vladimir
We introduce a new model of interacting spin 1/2. It describes interactions of three nearest neighbors. The Hamiltonian can be expressed in terms of Fredkin gates. The Fredkin gate (also known as the controlled swap gate) is a computational circuit suitable for reversible computing. Our construction generalizes the model presented by Peter Shor and Ramis Movassagh to half-integer spins. Our model can be solved by means of Catalan combinatorics in the form of random walks on the upper half plane of a square lattice (Dyck walks). Each Dyck path can be mapped on a wave function of spins. The ground state is an equally weighted superposition of Dyck walks (instead of Motzkin walks). We can also express it as a matrix product state. We further construct a model of interacting spins 3/2 and greater half-integer spins. The models with higher spins require coloring of Dyck walks. We construct a SU(k) symmetric model (where k is the number of colors). The leading term of the entanglement entropy is then proportional to the square root of the length of the lattice (like in the Shor-Movassagh model). The gap closes as a high power of the length of the lattice [5, 11].
Chudnovsky, Eugene M.
2007-01-01
An extension of Drude model is proposed that accounts for spin and spin-orbit interaction of charge carriers. Spin currents appear due to combined action of the external electric field, crystal field and scattering of charge carriers. The expression for spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, spin Hall conductivity $\\sigma_s$ and charge conductivity $\\sigma_c$ are related through $\\sigma_s = [2 \\pi \\hbar...
Huang, Biao; Kim, Yong Baek; Lu, Yuan-Ming
2017-02-01
Na4Ir3O8 provides a material platform to study three-dimensional quantum spin liquids in the geometrically frustrated hyperkagome lattice of Ir4 + ions. In this work, we consider quantum spin liquids on a hyperkagome lattice for generic spin models, focusing on the effects of anisotropic spin interactions. In particular, we classify possible Z2 and U (1 ) spin liquid states, following the projective symmetry group analysis in the slave-fermion representation. There are only three distinct Z2 spin liquids, together with 2 different U (1 ) spin liquids. The nonsymmorphic space group symmetry of the hyperkagome lattice plays a vital role in simplifying the classification, forbidding "π -flux" or "staggered-flux" phases in contrast to symmorphic space groups. We further prove that both U (1 ) states and one Z2 state among all 3 are symmetry-protected gapless spin liquids, robust against any symmetry-preserving perturbations. Motivated by the "spin-freezing" behavior recently observed in Na4Ir3O8 at low temperatures, we further investigate the nearest-neighbor spin model with the dominant Heisenberg interaction subject to all possible anisotropic perturbations from spin-orbit couplings. We find that a U (1 ) spin liquid ground state with spinon Fermi surfaces is energetically favored over Z2 states. Among all spin-orbit coupling terms, we show that only the Dzyaloshinskii-Moriya interaction can induce spin anisotropy in the ground state when perturbing from the isotropic Heisenberg limit. Our work paves the way for a systematic study of quantum spin liquids in various materials with a hyperkagome crystal structure.
Mayhall, Nicholas J.; Head-Gordon, Martin
2014-01-01
We highlight a simple strategy for computing the magnetic coupling constants, J, for a complex containing two multiradical centers. On the assumption that the system follows Heisenberg Hamiltonian physics, J is obtained from a spin-flip electronic structure calculation where only a single electron is excited (and spin-flipped), from the single reference with maximum S ^ z , M, to the M − 1 manifold, regardless of the number of unpaired electrons, 2M, on the radical centers. In an active space picture involving 2M orbitals, only one β electron is required, together with only one α hole. While this observation is extremely simple, the reduction in the number of essential configurations from exponential in M to only linear provides dramatic computational benefits. This (M, M − 1) strategy for evaluating J is an unambiguous, spin-pure, wave function theory counterpart of the various projected broken symmetry density functional theory schemes, and likewise gives explicit energies for each possible spin-state that enable evaluation of properties. The approach is illustrated on five complexes with varying numbers of unpaired electrons, for which one spin-flip calculations are used to compute J. Some implications for further development of spin-flip methods are discussed
Spin-isotropic continuum of spin excitations in antiferromagnetically ordered Fe1.07Te
Song, Yu; Lu, Xingye; Regnault, L.-P.; Su, Yixi; Lai, Hsin-Hua; Hu, Wen-Jun; Si, Qimiao; Dai, Pengcheng
2018-02-01
Unconventional superconductivity typically emerges in the presence of quasidegenerate ground states, and the associated intense fluctuations are likely responsible for generating the superconducting state. Here we use polarized neutron scattering to study the spin space anisotropy of spin excitations in Fe1.07Te exhibiting bicollinear antiferromagnetic (AF) order, the parent compound of FeTe1 -xSex superconductors. We confirm that the low-energy spin excitations are transverse spin waves, consistent with a local-moment origin of the bicollinear AF order. While the ordered moments lie in the a b plane in Fe1.07Te , it takes less energy for them to fluctuate out of plane, similar to BaFe2As2 and NaFeAs. At energies above E ≳20 meV, we find magnetic scattering to be dominated by an isotropic continuum that persists up to at least 50 meV. Although the isotropic spin excitations cannot be ascribed to spin waves from a long-range-ordered local-moment antiferromagnet, the continuum can result from the bicollinear magnetic order ground state of Fe1.07Te being quasidegenerate with plaquette magnetic order.
Single-spin addressing in an atomic Mott insulator
Weitenberg, Christof; Endres, Manuel; Sherson, Jacob
2011-01-01
directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line, and observed that our addressing scheme leaves the atoms in the motional ground state. The results should enable studies of entropy transport and the quantum dynamics of spin impurities...... and quantum spin dynamics. Here we demonstrate how such control can be implemented at the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator...... with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We...
Donor-driven spin relaxation in multivalley semiconductors.
Song, Yang; Chalaev, Oleg; Dery, Hanan
2014-10-17
The observed dependence of spin relaxation on the identity of the donor atom in n-type silicon has remained without explanation for decades and poses a long-standing open question with important consequences for modern spintronics. Taking into account the multivalley nature of the conduction band in silicon and germanium, we show that the spin-flip amplitude is dominated by short-range scattering off the central-cell potential of impurities after which the electron is transferred to a valley on a different axis in k space. Through symmetry arguments, we show that this spin-flip process can strongly affect the spin relaxation in all multivalley materials in which time-reversal cannot connect distinct valleys. From the physical insights gained from the theory, we provide guidelines to significantly enhance the spin lifetime in semiconductor spintronics devices.
Spin-current emission governed by nonlinear spin dynamics.
Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya
2015-10-16
Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.
Current interactions from the one-form sector of nonlinear higher-spin equations
Gelfond, O. A.; Vasiliev, M. A.
2018-06-01
The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.
Two-spinor description of massive particles and relativistic spin projection operators
Isaev, A. P.; Podoinitsyn, M. A.
2018-04-01
On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.
Spin Torques in Systems with Spin Filtering and Spin Orbit Interaction
Ortiz Pauyac, Christian
2016-06-19
In the present thesis we introduce the reader to the ﬁeld of spintronics and explore new phenomena, such as spin transfer torques, spin ﬁltering, and three types of spin-orbit torques, Rashba, spin Hall, and spin swapping, which have emerged very recently and are promising candidates for a new generation of memory devices in computer technology. A general overview of these phenomena is presented in Chap. 1. In Chap. 2 we study spin transfer torques in tunnel junctions in the presence of spin ﬁltering. In Chap. 3 we discuss the Rashba torque in ferromagnetic ﬁlms, and in Chap. 4 we study spin Hall eﬀect and spin swapping in ferromagnetic ﬁlms, exploring the nature of spin-orbit torques based on these mechanisms. Conclusions and perspectives are summarized in Chap. 5.
Tuckerman, Mark E; Alejandre, Jose; Lopez-Rendon, Roberto; Jochim, Andrea L; Martyna, Glenn J
2006-01-01
The constant-pressure, constant-temperature (NPT) molecular dynamics approach is re-examined from the viewpoint of deriving a new measure-preserving reversible geometric integrator for the equations of motion. The underlying concepts of non-Hamiltonian phase-space analysis, measure-preserving integrators and the symplectic property for Hamiltonian systems are briefly reviewed. In addition, current measure-preserving schemes for the constant-volume, constant-temperature ensemble are also reviewed. A new geometric integrator for the NPT method is presented, is shown to preserve the correct phase-space volume element and is demonstrated to perform well in realistic examples. Finally, a multiple time-step version of the integrator is presented for treating systems with motion on several time scales
Causality, spin, and equal-time commutators
Abdel-Rahman, A.M.
1975-01-01
We study the causality constraints on the structure of the Lorentz-antisymmetric component of the commutator of two conserved isovector currents between fermion states of equal momenta. We discuss the sum rules that follow from causality and scaling, using the recently introduced refined infinite-momentum technique. The complete set of sum rules is found to include the spin-dependent fixed-mass sum rules obtained from light-cone commutators. The causality and scaling restrictions on the structure of the electromagnetic equal-time commutators are discussed, and it is found, in particular, that causality requires the spin-dependent part of the matrix element for the time-space electromagnetic equal-time commutator to vanish identically. It is also shown, in comparison with the electromagnetic case, that the corresponding matrix element for the time-space isovector current equal-time commutator is required, by causality, to have isospin-antisymmetric tensor and scalar operator Schwinger terms
Optical spin generation/detection and spin transport lifetimes
Miah, M. Idrish
2011-01-01
We generate electron spins in semiconductors by optical pumping. The detection of them is also performed by optical technique using time-resolved pump-probe photoluminescence polarization measurements in the presence of an external magnetic field perpendicular to the generated spin. The spin polarization in dependences of the pulse length, pump-probe delay and external magnetic field is studied. From the dependence of spin-polarization on the delay of the probe, the electronic spin transport lifetimes and the spin relaxation frequencies as a function of the strength of the magnetic field are estimated. The results are discussed based on hyperfine effects for interacting electrons.
Optical spin generation/detection and spin transport lifetimes
Miah, M. Idrish, E-mail: m.miah@griffith.edu.au [Department of Physics, University of Chittagong, Chittagong 4331 (Bangladesh)
2011-02-25
We generate electron spins in semiconductors by optical pumping. The detection of them is also performed by optical technique using time-resolved pump-probe photoluminescence polarization measurements in the presence of an external magnetic field perpendicular to the generated spin. The spin polarization in dependences of the pulse length, pump-probe delay and external magnetic field is studied. From the dependence of spin-polarization on the delay of the probe, the electronic spin transport lifetimes and the spin relaxation frequencies as a function of the strength of the magnetic field are estimated. The results are discussed based on hyperfine effects for interacting electrons.
Magnetocaloric effect in quantum spin-s chains
A. Honecker
2009-01-01
Full Text Available We compute the entropy of antiferromagnetic quantum spin-s chains in an external magnetic field using exact diagonalization and Quantum Monte Carlo simulations. The magnetocaloric effect, i. e., temperature variations during adiabatic field changes, can be derived from the isentropes. First, we focus on the example of the spin-s=1 chain and show that one can cool by closing the Haldane gap with a magnetic field. We then move to quantum spin-s chains and demonstrate linear scaling with s close to the saturation field. In passing, we propose a new method to compute many low-lying excited states using the Lanczos recursion.
Rotational Invariance of the 2d Spin - Spin Correlation Function
Pinson, Haru
2012-09-01
At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3-5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22-26, 1984, JINR, vol II, pp 138-151, 1985).
Production of entropy on simplified dynamics in spin glass systems
Saakyan, D B
2001-01-01
In models of spin glasses one eliminates condition of extreme based on one of the order parameters. On the basis of the available expression for static sum one derived the effective hamiltonian for parameter and the appropriate energy. Relaxation of the system is studied as energy exchange between the degree of freedom related to the order slow parameter and with the rest of the system. At that level one may indicate point of glass capture within phase space on the basis of the static solutions. One studies p-spin model without magnetic field in case of replica symmetry violation. One studies dynamics of p-spin glass in magnetic field in replica-symmetrical phase. One studied model of spins with quadratic interaction when dynamic constants had temperature differing from temperature of space
General relativity with spin and torsion: Foundations and prospects
Hehl, F.W.; von der Heyde, P.; Kerlick, G.D.; Nester, J.M.
1976-01-01
A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the U 4 theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction mediated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the U 4 theory arises as a local gauge theory for the Poincare group in space-time. The deviations of the U 4 theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed
Efficient Spin Injection into Semiconductor
Nahid, M.A.I.
2010-06-01
Spintronic research has made tremendous progress nowadays for making future devices obtain extra advantages of low power, and faster and higher scalability compared to present electronic devices. A spintronic device is based on the transport of an electron's spin instead of charge. Efficient spin injection is one of the very important requirements for future spintronic devices. However, the effective spin injection is an exceedingly difficult task. In this paper, the importance of spin injection, basics of spin current and the essential requirements of spin injection are illustrated. The experimental technique of electrical spin injection into semiconductor is also discussed based on the experimental experience. The electrical spin injection can easily be implemented for spin injection into any semiconductor. (author)
Next-order spin-orbit contributions to chaos in compact binaries
Wang Yuzhao; Wu Xin
2011-01-01
This paper is mainly devoted to numerically investigating the effects of the next-order spin-orbit interactions including the 2.5 post-Newtonian order term of the equations of motion and the second post-Newtonian order terms of the spin precession equations on chaos in the conservative Lagrangian dynamics of a spinning compact binary system. It is shown sufficiently through individual orbit simulations, the dependence of the invariant fast Lyapunov indicators on the variations of initial spin angles and the phase space scans for chaos, that the next-order spin-orbit contributions do play an important role in the amplification of chaos.
The critical role of the barrier thickness in spin filter tunneling
Miller, Casey W.
2009-01-01
Spin filter tunneling is considered in the low bias limit as functions of the temperature dependent barrier parameters. We demonstrate the generation of spin polarized tunneling currents in relation to the magnetic order parameter, and discuss how an interfacially suppressed order parameter leads to a temperature dependent tunneling current asymmetry. Analyzing the full parameter space reveals that the often overlooked barrier thickness plays a critical role in spin filter tunneling. With all else fixed, thicker barriers yield higher spin polarization, and allow a given polarization to be achieved at higher temperatures. This insight may open the door for new materials to serve as spin filter barriers.
Spin-waves in antiferromagnetic single crystal LiFePO$_4$
Li, Jiying; Garlea, Vasile O.; Zarestky, Jerel L.; Vaknin, David
2005-01-01
Spin-wave dispersions in the antiferromagnetic state of single crystal LiFePO$_4$ were determined by inelastic neutron scattering measurements. The dispersion curves measured from the (010) reflection along both {\\it a}$^\\ast$ and {\\it b}$^\\ast$ reciprocal-space directions reflect the anisotropic coupling of the layered Fe$^{2+}$ (S = 2) spin-system. The spin-wave dispersion curves were theoretically modeled using linear spin-wave theory by including in the spin-Hamiltonian in-plane nearest- ...
Yokosawa, A.
1992-01-01
Spin physics activities at medium and high energies became significantly active when polarized targets and polarized beams became accessible for hadron-hadron scattering experiments. My overview of spin physics will be inclined to the study of strong interaction using facilities at Argonne ZGS, Brookhaven AGS (including RHIC), CERN, Fermilab, LAMPF, an SATURNE. In 1960 accelerator physicists had already been convinced that the ZGS could be unique in accelerating a polarized beam; polarized beams were being accelerated through linear accelerators elsewhere at that time. However, there was much concern about going ahead with the construction of a polarized beam because (i) the source intensity was not high enough to accelerate in the accelerator, (ii) the use of the accelerator would be limited to only polarized-beam physics, that is, proton-proton interaction, and (iii) p-p elastic scattering was not the most popular topic in high-energy physics. In fact, within spin physics, π-nucleon physics looked attractive, since the determination of spin and parity of possible πp resonances attracted much attention. To proceed we needed more data beside total cross sections and elastic differential cross sections; measurements of polarization and other parameters were urgently needed. Polarization measurements had traditionally been performed by analyzing the spin of recoil protons. The drawbacks of this technique are: (i) it involves double scattering, resulting in poor accuracy of the data, and (ii) a carbon analyzer can only be used for a limited region of energy
Leading Twist GPDs and Transverse Spin Densities in a Proton
Mondal, Chandan; Maji, Tanmay; Chakrabarti, Dipankar; Zhao, Xingbo
2018-05-01
We present a study of both chirally even and odd generalized parton distributions in the leading twist for the quarks in a proton using the light-front wavefunctions of a quark-diquark model predicted by the holographic QCD. For transversely polarized proton, both chiral even and chiral odd GPDs contribute to the spin densities which are related to the GPDs in transverse impact parameter space. Here, we also present a study of the spin densities for transversely polarized quark and proton.
Noise in tunneling spin current across coupled quantum spin chains
Aftergood, Joshua; Takei, So
2018-01-01
We theoretically study the spin current and its dc noise generated between two spin-1 /2 spin chains weakly coupled at a single site in the presence of an over-population of spin excitations and a temperature elevation in one subsystem relative to the other, and we compare the corresponding transport quantities across two weakly coupled magnetic insulators hosting magnons. In the spin chain scenario, we find that applying a temperature bias exclusively leads to a vanishing spin current and a concomitant divergence in the spin Fano factor, defined as the spin current noise-to-signal ratio. This divergence is shown to have an exact analogy to the physics of electron scattering between fractional quantum Hall edge states and not to arise in the magnon scenario. We also reveal a suppression in the spin current noise that exclusively arises in the spin chain scenario due to the fermion nature of the spin-1/2 operators. We discuss how the spin Fano factor may be extracted experimentally via the inverse spin Hall effect used extensively in spintronics.
Higher point spin field correlators in D=4 superstring theory
Haertl, D.; Schlotterer, O.; Stieberger, S.
2010-01-01
Calculational tools are provided allowing to determine general tree-level scattering amplitudes for processes involving bosons and fermions in heterotic and superstring theories in four space-time dimensions. We compute higher-point superstring correlators involving massless four-dimensional fermionic and spin fields. In D=4 these correlators boil down to a product of two pure spin field correlators of left- and right-handed spin fields. This observation greatly simplifies the computation of such correlators. The latter are basic ingredients to compute multi-fermion superstring amplitudes in D=4. Their underlying fermionic structure and the fermionic couplings in the effective action are determined by these correlators.
Frequency selective tunable spin wave channeling in the magnonic network
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Odincov, S. A.; Sheshukova, S. E.; Sharaevskii, Yu. P. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Stognij, A. I. [Scientific-Practical Materials Research Center, National Academy of Sciences of Belarus, 220072 Minsk (Belarus)
2016-04-25
Using the space-resolved Brillouin light scattering spectroscopy, we study the frequency and wavenumber selective spin-wave channeling. We demonstrate the frequency selective collimation of spin-wave in an array of magnonic waveguides, formed between the adjacent magnonic crystals on the surface of yttrium iron garnet film. We show the control over spin-wave propagation length by the orientation of an in-plane bias magnetic field. Fabricated array of magnonic crystal can be used as a magnonic platform for multidirectional frequency selective signal processing applications in magnonic networks.
On the spin-dependent sensitivity of XENON100
Garny, Mathias [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Ibarra, Alejandro; Pato, Miguel; Vogl, Stefan [Technische Univ. Muenchen, Garching (Germany). Physik-Department
2012-11-15
The latest XENON100 data severely constrains dark matter elastic scattering off nuclei, leading to impressive upper limits on the spin-independent cross-section. The main goal of this paper is to stress that the same data set has also an excellent spin-dependent sensitivity, which is of utmost importance in probing dark matter models. We show in particular that the constraints set by XENON100 on the spin-dependent neutron cross-section are by far the best at present, whereas the corresponding spin-dependent proton limits lag behind other direct detection results. The effect of nuclear uncertainties on the structure functions of xenon isotopes is analysed in detail and found to lessen the robustness of the constraints, especially for spin-dependent proton couplings. Notwith-standing, the spin-dependent neutron prospects for XENON1T and DARWIN are very encouraging. We apply our constraints to well-motivated dark matter models and demonstrate that in both mass-degenerate scenarios and the minimal supersymmetric standard model the spin-dependent neutron limits can actually override the spin-independent limits. This opens the possibility of probing additional unexplored regions of the dark matter parameter space with the next generation of ton-scale direct detection experiments.
On the spin-dependent sensitivity of XENON100
Garny, Mathias; Ibarra, Alejandro; Pato, Miguel; Vogl, Stefan
2012-11-01
The latest XENON100 data severely constrains dark matter elastic scattering off nuclei, leading to impressive upper limits on the spin-independent cross-section. The main goal of this paper is to stress that the same data set has also an excellent spin-dependent sensitivity, which is of utmost importance in probing dark matter models. We show in particular that the constraints set by XENON100 on the spin-dependent neutron cross-section are by far the best at present, whereas the corresponding spin-dependent proton limits lag behind other direct detection results. The effect of nuclear uncertainties on the structure functions of xenon isotopes is analysed in detail and found to lessen the robustness of the constraints, especially for spin-dependent proton couplings. Notwith-standing, the spin-dependent neutron prospects for XENON1T and DARWIN are very encouraging. We apply our constraints to well-motivated dark matter models and demonstrate that in both mass-degenerate scenarios and the minimal supersymmetric standard model the spin-dependent neutron limits can actually override the spin-independent limits. This opens the possibility of probing additional unexplored regions of the dark matter parameter space with the next generation of ton-scale direct detection experiments.
Spin Structures in Magnetic Nanoparticles
Mørup, Steen; Brok, Erik; Frandsen, Cathrine
2013-01-01
Spin structures in nanoparticles of ferrimagnetic materials may deviate locally in a nontrivial way from ideal collinear spin structures. For instance, magnetic frustration due to the reduced numbers of magnetic neighbors at the particle surface or around defects in the interior can lead to spin...... canting and hence a reduced magnetization. Moreover, relaxation between almost degenerate canted spin states can lead to anomalous temperature dependences of the magnetization at low temperatures. In ensembles of nanoparticles, interparticle exchange interactions can also result in spin reorientation....... Here, we give a short review of anomalous spin structures in nanoparticles....
Quantum mechanics on phase space: The hydrogen atom and its Wigner functions
Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.
2018-03-01
Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.
Rackham, Neil
1995-01-01
True or false? In selling high-value products or services: "closing" increases your chance of success; it is essential to describe the benefits of your product or service to the customer; objection handling is an important skill; and open questions are more effective than closed questions. All false, says Neil Rackham. He and his team studied more than 35,000 sales calls made by 10,000 sales people in 23 countries over 12 years. Their findings revealed that many of the methods developed for selling low-value goods just don't work for major sales. Rackham went on to introduce his SPIN-selling method, where SPIN describes the whole selling process - Situation questions, Problem questions, Implication questions, Need-payoff questions. SPIN-selling provides you with a set of simple and practical techniques which have been tried in many of today's leading companies with dramatic improvements to their sales performance.
Contucci, Pierluigi
2013-01-01
Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.
Exertional Rhabdomyolysis after Spinning.
Jeong, Youjin; Kweon, Hyuk-Jung; Oh, Eun-Jung; Ahn, Ah-Leum; Choi, Jae-Kyung; Cho, Dong-Yung
2016-11-01
Any strenuous muscular exercise may trigger rhabdomyolysis. We report an episode of clinically manifested exertional rhabdomyolysis due to stationary cycling, commonly known as spinning. Reports of spinning-related rhabdomyolysis are rare in the English literature, and the current case appears to be the first such case reported in South Korea. A previously healthy 21-year-old Asian woman presented with severe thigh pain and reddish-brown urinary discoloration 24-48 hours after attending a spinning class at a local gymnasium. Paired with key laboratory findings, her symptoms were suggestive of rhabdomyolysis. She required hospital admission to sustain renal function through fluid resuscitation therapy and fluid balance monitoring. Because exertional rhabdomyolysis may occur in any unfit but otherwise healthy individual who indulges in stationary cycling, the potential health risks of this activity must be considered.
Jensen, J.; Houmann, Jens Christian Gylden
1975-01-01
The selection rules for the linear couplings between magnons and phonons propagating in the c direction of a simple basal-plane hcp ferromagnet are determined by general symmetry considerations. The acoustic-optical magnon-phonon interactions observed in the heavy-rare-earth metals have been...... explained by Liu as originating from the mixing of the spin states of the conduction electrons due to the spin-orbit coupling. We find that this coupling mechanism introduces interactions which violate the selection rules for a simple ferromagnet. The interactions between the magnons and phonons propagating...... in the c direction of Tb have been studied experimentally by means of inelastic neutron scattering. The magnons are coupled to both the acoustic- and optical-transverse phonons. By studying the behavior of the acoustic-optical coupling, we conclude that it is a spin-mixed-induced coupling as proposed...
Schill, Christian
2012-01-01
The COMPASS experiment is a fixed target experiment at the CERN SPS using muon and hadron beams for the investigation of the spin structure of the nucleon and hadron spectroscopy. The main objective of the muon physics program is the study of the spin of the nucleon in terms of its constituents, quarks and gluons. COMPASS has accumulated data during 6 years scattering polarized muons off longitudinally or transversely polarized deuteron ( 6 LiD) or proton (NH 3 ) targets. Results for the gluon polarization are obtained from longitudinal double spin cross section asymmetries using two different channels, open charm production and high transverse momentum hadron pairs, both proceeding through the photon-gluon fusion process. Also, the longitudinal spin structure functions of the proton and the deuteron were measured in parallel as well as the helicity distributions for the three lightest quark flavours. With a transversely polarized target, results were obtained with proton and deuteron targets for the Collins and Sivers asymmetries for charged hadrons as well as for identified kaons and pions. The Collins asymmetry is sensitive to the transverse spin structure of the nucleon, while the Sivers asymmetry reflects correlations between the quark transverse momentum and the nucleon spin. Recently, a new proposal for the COMPASS II experiment was accepted by the CERN SPS which includes two new topics: Exclusive reactions like DVCS and DVMP using the muon beam and a hydrogen target to study generalized parton distributions and Drell-Yan measurements using a pion beam and a polarized NH 3 target to study transverse momentum dependent distributions.
Control of electron spin decoherence in nuclear spin baths
Liu, Ren-Bao
2011-03-01
Nuclear spin baths are a main mechanism of decoherence of spin qubits in solid-state systems, such as quantum dots and nitrogen-vacancy (NV) centers of diamond. The decoherence results from entanglement between the electron and nuclear spins, established by quantum evolution of the bath conditioned on the electron spin state. When the electron spin is flipped, the conditional bath evolution is manipulated. Such manipulation of bath through control of the electron spin not only leads to preservation of the center spin coherence but also demonstrates quantum nature of the bath. In an NV center system, the electron spin effectively interacts with hundreds of 13 C nuclear spins. Under repeated flip control (dynamical decoupling), the electron spin coherence can be preserved for a long time (> 1 ms) . Thereforesomecharacteristicoscillations , duetocouplingtoabonded 13 C nuclear spin pair (a dimer), are imprinted on the electron spin coherence profile, which are very sensitive to the position and orientation of the dimer. With such finger-print oscillations, a dimer can be uniquely identified. Thus, we propose magnetometry with single-nucleus sensitivity and atomic resolution, using NV center spin coherence to identify single molecules. Through the center spin coherence, we could also explore the many-body physics in an interacting spin bath. The information of elementary excitations and many-body correlations can be extracted from the center spin coherence under many-pulse dynamical decoupling control. Another application of the preserved spin coherence is identifying quantumness of a spin bath through the back-action of the electron spin to the bath. We show that the multiple transition of an NV center in a nuclear spin bath can have longer coherence time than the single transition does, when the classical noises due to inhomogeneous broadening is removed by spin echo. This counter-intuitive result unambiguously demonstrates the quantumness of the nuclear spin bath
Bland, L.C.
2003-01-01
The physics goals that will be addressed by colliding polarized protons at the Relativistic Heavy Ion Collider (RHIC) are described. The RHIC spin program provides a new generation of experiments that will unfold the quark, anti-quark and gluon contributions to the proton's spin. In addition to these longer term goals, this paper describes what was learned from the first polarized proton collisions at √(s)=200 GeV. These collisions took place in a five-week run during the second year of RHIC operation
CONFERENCE: Muon spin rotation
Karlsson, Erik
1986-11-15
An international physics conference centred on muons without a word about leptons, weak interactions, EMC effects, exotic decay modes or any other standard high energy physics jargon. Could such a thing even have been imagined ten years ago? Yet about 120 physicists and chemists from 16 nations gathered at the end of June in Uppsala (Sweden) for their fourth meeting on Muon Spin Rotation, Relaxation and Resonance, without worrying about the muon as an elementary particle. This reflects how the experimental techniques based on the muon spin interactions have reached maturity and are widely recognized by condensed matter physicists and specialized chemists as useful tools.
Jensen, J.; Houmann, Jens Christian Gylden; Bjerrum Møller, Hans
1975-01-01
with the symmetry, we deduce the dispersion relation for the spin waves in a basal-plane ferromagnet. This phenomenological spin-wave theory accounts for the observed behavior of the magnon energies in Tb. The two q⃗-dependent Bogoliubov components of the magnon energies are derived from the experimental results......, which are corrected for the effect of the direct coupling between the magnons and the phonons, and for the field dependence of the relative magnetization at finite temperatures. A large q⃗-dependent difference between the two energy components is observed, showing that the anisotropy of the two...
Ramachandran, R.
1994-09-01
The object of this brief review is to reconcile different points of view on how the spin of proton is made up from its constituents. On the basis of naive quark model with flavour symmetry such as isospin or SU(3) one finds a static description. On the contrary the local SU(3) colour symmetry gives a dynamical view. Both these views are contrasted and the role of U(1) axial anomaly and the ambiguity for the measurable spin content is discussed. (author). 16 refs, 1 fig
Simulation of electron spin resonance spectroscopy in diverse environments: An integrated approach
Zerbetto, Mirco; Polimeno, Antonino; Barone, Vincenzo
2009-12-01
We discuss in this work a new software tool, named E-SpiReS (Electron Spin Resonance Simulations), aimed at the interpretation of dynamical properties of molecules in fluids from electron spin resonance (ESR) measurements. The code implements an integrated computational approach (ICA) for the calculation of relevant molecular properties that are needed in order to obtain spectral lines. The protocol encompasses information from atomistic level (quantum mechanical) to coarse grained level (hydrodynamical), and evaluates ESR spectra for rigid or flexible single or multi-labeled paramagnetic molecules in isotropic and ordered phases, based on a numerical solution of a stochastic Liouville equation. E-SpiReS automatically interfaces all the computational methodologies scheduled in the ICA in a way completely transparent for the user, who controls the whole calculation flow via a graphical interface. Parallelized algorithms are employed in order to allow running on calculation clusters, and a web applet Java has been developed with which it is possible to work from any operating system, avoiding the problems of recompilation. E-SpiReS has been used in the study of a number of different systems and two relevant cases are reported to underline the promising applicability of the ICA to complex systems and the importance of similar software tools in handling a laborious protocol. Program summaryProgram title: E-SpiReS Catalogue identifier: AEEM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEM_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL v2.0 No. of lines in distributed program, including test data, etc.: 311 761 No. of bytes in distributed program, including test data, etc.: 10 039 531 Distribution format: tar.gz Programming language: C (core programs) and Java (graphical interface) Computer: PC and Macintosh Operating system: Unix and Windows Has the code been vectorized or
Chang, Zhiwei; Halle, Bertil
2013-10-14
In complex biological or colloidal samples, magnetic relaxation dispersion (MRD) experiments using the field-cycling technique can characterize molecular motions on time scales ranging from nanoseconds to microseconds, provided that a rigorous theory of nuclear spin relaxation is available. In gels, cross-linked proteins, and biological tissues, where an immobilized macromolecular component coexists with a mobile solvent phase, nuclear spins residing in solvent (or cosolvent) species relax predominantly via exchange-mediated orientational randomization (EMOR) of anisotropic nuclear (electric quadrupole or magnetic dipole) couplings. The physical or chemical exchange processes that dominate the MRD typically occur on a time scale of microseconds or longer, where the conventional perturbation theory of spin relaxation breaks down. There is thus a need for a more general relaxation theory. Such a theory, based on the stochastic Liouville equation (SLE) for the EMOR mechanism, is available for a single quadrupolar spin I = 1. Here, we present the corresponding theory for a dipole-coupled spin-1/2 pair. To our knowledge, this is the first treatment of dipolar MRD outside the motional-narrowing regime. Based on an analytical solution of the spatial part of the SLE, we show how the integral longitudinal relaxation rate can be computed efficiently. Both like and unlike spins, with selective or non-selective excitation, are treated. For the experimentally important dilute regime, where only a small fraction of the spin pairs are immobilized, we obtain simple analytical expressions for the auto-relaxation and cross-relaxation rates which generalize the well-known Solomon equations. These generalized results will be useful in biophysical studies, e.g., of intermittent protein dynamics. In addition, they represent a first step towards a rigorous theory of water (1)H relaxation in biological tissues, which is a prerequisite for unravelling the molecular basis of soft