Academic literature on the topic 'Rotor/spin-wave separation of variables'

To introduce Soliton theory in magnetic recording systems, we begin with the profile of Domain Wall, which is key elements of recording systems, knowing that many different Domain Walls shape exist. For this, we consider the recording media as chain of atoms (spin) and, we use the Hamiltonian to describe the global state of the system; by taking into consideration interaction between the neighboring spin and anisotropic interaction. Spins are considered as classical vector; for that, we defined the cosine and sine of angles that specify the position of the spins. They are developed in Taylor’s series until second order then using the approximation of continuous medium we obtained the Lagragian relation. This Lagragian enables us to describe the dynamics of spin through the wave velocity. As we are fine just the profile of domain wall it is beneficial for us to consider the wall at rest (static) and by the aid of Euler equation we obtain two simple equations; using the equilibrium conditions, the differential equation is obtained and solved by the quadratic method and separation variables method. The profile of domain wall that we obtain is at a particular position, then analytical and numerical simulation give us the opportunity to see that profile of that domain wall is a Kink, anti-Kink Soliton and also Soliton Train. Using this magnetic Soliton wave (Domain Wall), we also evaluate the playback voltage V (x), the peak voltage and the half pulse width PW50 to confirm the uses of this DW profile in magnetic recording systems and insure validity of this work.

We study the St¨uckelberg equation for a relativistic particle with two spin states S = 1 and S = 0 in the presence of an external uniform magnetic field. The particle is described by an 11-component wave function consisting of a scalar, a vector, and an antisymmetric tensor. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, a system for 11 radial functions is obtained. Its solution is based on the use of the Fedorov-Gronsky method, in which all 11 radial functions are expressed in terms of three main functions. Exact solutions with cylindrical symmetry are constructed. Three series of energy levels are found.

The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.

A time-dependent self-adjoint even Hamiltonian is defined by a linear combination of generators of the semidirect sum [Formula: see text], of the orthosymplectic plus the even Heisenberg algebra by computing the supercommutator of odd binary forms Π, given as linear combinations of odd bilinear generators of the odd Heisenberg algebra [Formula: see text] elements times [Formula: see text] elements, establishing a relationship between entangled boson systems and entangled fermion systems. This approach leads to the concept of intertwining, defined through the resulting quadratic Hamiltonians of bosons and, separately, of fermions with coefficients given in terms of the same coefficients of Π. Intertwining is invariant under transformations of Π, which leave certain binary forms of the coefficients of Π in the Hamiltonian unchanged. Alternatively, the coefficients can be interpreted as simultaneous time-dependent (super-) control parameters for both spin-statistics. Time-dependent inhomogeneous linear supercanonical transformations of wave vectors leave invariant the Heisenberg superalgebra [Formula: see text] and belong to the semidirect product Osp( m′/ n′) ⋉ N e( n′ + 1) of the orthosymplectic supergroup with the even Heisenberg group. The unitary time evolution operator is constructed using the adjoint map in canonical coordinates determined by the supercanonical transformation. The method is a generalization of an Inönu–Wigner contraction procedure and a Wei–Norman method for superalgebras with a selection of subalgebras associated with the root space decomposition of the Lie superalgebra. Analogously, this is a separation of variables method for quantum mechanical problems in systems with bosons and fermions. The standard Floquet theory leads to new results concerning stability for locally periodic coefficients. The lowest dimensional cases are explicitly computed. The intertwining of boson and fermions systems and the Hamiltonians considered here are of interest in quantum control theory for systems including fermions and bosons, in quantum optics, and quantum computation.

Based on the generalized dressing method, we propose a new integrable variable coefficient Spin-1 Gross–Pitaevskii equations and derive their Lax pair. Using separation of variables, we have derived explicit solutions of the equations. In order to analyze the characteristic of derived solution, the graphical wave of the solutions is plotted with the aid of Matlab.

Abstract In this paper we take further steps towards developing the separation of variables program for integrable spin chains with $$ \mathfrak{gl}(N) $$ gl N symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions and wave function overlaps in a simple determinant form. In particular, we show how an overlap between on-shell and off-shell algebraic Bethe states can be written as a determinant. Another result, particularly useful for AdS/CFT applications, is an overlap between two Bethe states with different twists, which also takes a determinant form in our approach. Our results also extend our previous works in collaboration with A. Cavaglia and D. Volin to general values of the spin, including the SoV construction in the higher-rank non-compact case for the first time.

We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the commuting conserved charges of the quantum integrable models to generate bases in which their spectral problem is separated, i.e. in which the wave functions are factorized in terms of specific solutions of a functional equation. For the so-called “non-fundamental” models we construct two different types of SoV bases. The first is given from the fundamental quantum Lax operator having isomorphic auxiliary and quantum spaces and that can be obtained by fusion of the original quantum Lax operator. The construction essentially follows the one we used previously for fundamental models and allows us to derive the simplicity and diagonalizability of the transfer matrix spectrum. Then, starting from the original quantum Lax operator and using the full tower of the fused transfer matrices, we introduce a second type of SoV bases for which the proof of the separation of the transfer matrix spectrum is naturally derived. We show that, under some special choice, this second type of SoV bases coincides with the one associated to Sklyanin’s approach. Moreover, we derive the finite difference type (quantum spectral curve) functional equation and the set of its solutions defining the complete transfer matrix spectrum. This is explicitly implemented for the integrable quantum models associated to the higher spin representations of the general quasi-periodic Y(gl_{2})Y(gl2) Yang-Baxter algebra. Our SoV approach also leads to the construction of a QQ-operator in terms of the fused transfer matrices. Finally, we show that the QQ-operator family can be equivalently used as the family of commuting conserved charges enabling to construct our SoV bases.

We consider the vector and the Lichnerowicz wave equations on the Schwarzschild spacetime, which correspond to the Maxwell and linearized Einstein equations in harmonic gauges (or, respectively, in Lorenz and de Donder gauges). After a complete separation of variables, the radial mode equations form complicated systems of coupled linear ODEs. We outline a precise abstract strategy to decouple these systems into sparse triangular form, where the diagonal blocks consist of spin-s scalar Regge-Wheeler equations (for spins s=0,1,2). Building on the example of the vector wave equation, which we have treated previously, we complete a successful implementation of our strategy for the Lichnerowicz wave equation. Our results go a step further than previous more ad-hoc attempts in the literature by presenting a full and maximally simplified final triangular form. These results have important applications to the quantum field theory of and the classical stability analysis of electromagnetic and gravitational perturbations of the Schwarzschild black hole in harmonic gauges.

Le problème quantique à N corps, notamment l’étude des propriétés dynamiques d’un système quantique composite est l’un des problèmes les plus durs de la physique moderne, car il y a peu de résultats analytiques et les méthodes numériques exactes requièrent des ressources numériques exponentielles en la taille du système. Dans cette thèse, nous avons étudié la mise en évidence de propriétés de corrélations et d’intrication pour des systèmes d’atomes magnétiques sur réseau, par exemple via la compression de spin. Pour cela nous avons mis au point de nouvelles méthodes numériques approchées, qui permettent de simuler des systèmes de grande taille. Cela nous a permis de proposer des protocoles qui permettent de générer de la compression de spin qui croit d’autant plus que le système est grand, ce qui a un double intérêt. D’une part, il s’agit d’un témoin d’intrication, qui permettrait donc de détecter de l’intrication dans un système d’atomes magnétiques, ce qui n’a pas encore été réalisée expérimentalement à ce jour. D’autre part la compression de spin présente un important intérêt métrologique, puisque les états comprimés permettent des mesures extrêmement précises de champs magnétiques par exemple, bien au-delà de ce qui est possible avec des atomes indépendants. Enfin, nous avons étudié la génération d’autres formes d'intrication, à savoir la compression à deux modes (de spin, ou d'impulsion), cette fois pour des systèmes d’atomes condensés. Connue dans le cas de condensats d’atomes de spin-1, nous avons proposé comment généraliser ce processus au cas de compression en impulsion, en utilisant un Hamiltonien modulé dans le temps. Les états intriqués ainsi produits sont potentiellement très intéressants dans la mesure à haute précision de forces inertielles
The quantum many-body problem, and especially the study of dynamical properties of a multipartite quantum system, is one of the hardest problems of modern physics. There exist only a few analytical results and exact numerical simulations require an amount of resources that grow exponentially with the system size.In this thesis, we studied correlations and entanglement properties for systems composed of magnetic atoms on a lattice, for instance via the generation of spin squeezing. For this purpose we have developed new approximate numerical methods that allow us to study large system sizes. This enabled us to propose protocols to generate an amount of spin squeezing that scales with the system size. The advantage is twofold. Since spin squeezing is an entanglement witness, this would allow for entanglement detection in a system of magnetic atoms - which has yet to be realized experimentally. Moreover, spin squeezing offers an important metrological advantage, asspin-squeezed states can be used for extremely precise measurements of external magnetic fields, far beyond what one can achieve within dependent atoms.Finally, we studied the generation of other forms of entanglement, namely Dicke squeezing (of spin or momentum), in systems of Bose condensed atoms. This form of entanglement is well-known in spin-1 atomic condensates. Here, we propose a protocol to generalize it to the case of momentum modes, using a time-dependent Hamiltonian. The entangled states generated during the dynamics are potentially useful for the precision measurements of inertial forces

Abstract Recently, cyclorotors, utilizing lift rather than buoyancy forces for energy extraction, have been proposed and inherit many of the appealing features characteristic of modern wind turbines. In particular, the ability to spill energy though foil pitching allows the device to remain at rated power despite significant variations in input power level, while additional cyclorotor features, including variable submergence depth and rotor radius, also permit a significant degree of modulation of the device structure, and energy absorption characteristics, offering considerable flexibility. These configuration flexibilities, in addition to torque control of the rotor/generator shaft (also characteristic of wind turbines) offers the control engineer considerable freedom in adjusting the device characteristics to maximise the effectiveness of the device in capturing wave power, while maintaining structural integrity and minimizing harmful stresses on system components. However, such flexibility also provides a significant challenge in the form of a multivariable control problem for a system described by significantly nonlinear hydrodynamics. This paper describes a proposed hierarchical control system for a cyclorotor wave energy device, utilizing submergence depth, rotor radius, foil pitch angles, and shaft torque as control inputs. The hierarchy involves the separation of the control actuators into two classes: structural (or slow) control effectors, and wave-by-wave (or fast) control effectors. In particular, the paper will examine the interaction between the two levels of the control hierarchy and the need, if any, for simultaneous optimisation of the control parameters at both levels.

The paper presents a new solution for the wind turbine profile shape modeling based on the concept of the maximum lift force, capable to be produced at different values of the wind velocities. The profile is designed and realized in accordance with the new concept emerged in the last decade, on the operation of the wind turbines with maximum lifting force. The purpose is to provide a low-noise during operation because a negative effect on the medium and long-term operation of the wind turbines (wind farms) is the noise that affects the flight of birds, terrestrial animal life, and especially human communities. Various sources generate independent acoustic emissions on wind profiles, such as the turbulent flow, the interaction of the turbulent boundary layer area of the trailing edge, the flow separation, and the boundary layer separation of vortices formed in the zone of the trailing edge. There is also considered the influence of the apparent wind on the incidence variation of the profile. In order to maintain an optimum angle of attack relative to the wind velocity, a fixed blade inclination must increase its speed to be proportional to the wind. Thus, to maximize the aerodynamic performance, the rotor must spin faster when the wind intensity increases. Measurement of the acoustic signal requires electronic devices that operate on electric signals obtained from the conversion of the pressure variations in voltage or variations in electrical current. The noise caused by the turbulent flow is generated primarily by the sharply pointed leading edge and cannot be diminished. There are presented some numerical results correlated with the measurements made in the field.