Solution of the Lindblad equation for spin helix states arXiv
... superdiffusive nonequilibrium stationary states “spin helix states” (SHS), in analogy to phenomena in spin-orbit-coupled two-dimensional electron systems [4, 5, 6]. We focus on one-dimensional spin chains, which are of great current interest. However, it will transpire that analogous SHS will appear ...
... superdiffusive nonequilibrium stationary states “spin helix states” (SHS), in analogy to phenomena in spin-orbit-coupled two-dimensional electron systems [4, 5, 6]. We focus on one-dimensional spin chains, which are of great current interest. However, it will transpire that analogous SHS will appear ...
Chapter 2. Electronic, Vibrational and Spin
... “Hamiltonian” operator and corresponds to a mathematical “operator” (a mathematical procedure that changes one function into another) for the possible energies of the system. These energies may be the electronic energies of the molecule, the vibration energies of the molecule or the spin energies of ...
... “Hamiltonian” operator and corresponds to a mathematical “operator” (a mathematical procedure that changes one function into another) for the possible energies of the system. These energies may be the electronic energies of the molecule, the vibration energies of the molecule or the spin energies of ...
Heisenberg Spin Chains : from Quantum Groups to
... called dynamical structure factor (the Fourier transform of the dynamical two-point correlation function). The importance of these functions originates from the following facts : (i) They can be measured directly via scattering of neutrons or photons at the material to be studied [1, 2, 3, 4, 5, 7, ...
... called dynamical structure factor (the Fourier transform of the dynamical two-point correlation function). The importance of these functions originates from the following facts : (i) They can be measured directly via scattering of neutrons or photons at the material to be studied [1, 2, 3, 4, 5, 7, ...
Spin-current-induced charge accumulation and electric
... central region, and km is the wave vector along the semiinfinite lead. Here, we assume that there is no spin-orbit coupling in the leads. This not only guarantees that the spin currents under our investigation is well defined from the experimental aspect, but also is justified because it turns out t ...
... central region, and km is the wave vector along the semiinfinite lead. Here, we assume that there is no spin-orbit coupling in the leads. This not only guarantees that the spin currents under our investigation is well defined from the experimental aspect, but also is justified because it turns out t ...
Statistical Physics
... Equation of state The dynamics of particles and their interactions were understood at the classical level by the establishment of Newton’s laws. Later, these had to be slightly modified with the introduction of Einstein’s theory of relativity. A complete reformulation of mechanics became necessary w ...
... Equation of state The dynamics of particles and their interactions were understood at the classical level by the establishment of Newton’s laws. Later, these had to be slightly modified with the introduction of Einstein’s theory of relativity. A complete reformulation of mechanics became necessary w ...
n - at www.arxiv.org.
... oscillators. Though being simple, the model provides the basis for the description of solidstate crystals in which deviations of the lattice atoms from their equilibrium positions are described in terms of harmonical oscillators. In this paper we study possible stationary quantum dissipative structu ...
... oscillators. Though being simple, the model provides the basis for the description of solidstate crystals in which deviations of the lattice atoms from their equilibrium positions are described in terms of harmonical oscillators. In this paper we study possible stationary quantum dissipative structu ...
Entanglement with Negative Wigner Function of Almost 3000 Atoms
... classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise. Non-Gaussian states with a negative Wigner function are however manifestly non-classical, since the Wigner function as a quasiprobability function must remain non-negative in the classical realm. ...
... classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise. Non-Gaussian states with a negative Wigner function are however manifestly non-classical, since the Wigner function as a quasiprobability function must remain non-negative in the classical realm. ...
Lecture Notes in Quantum Mechanics Doron Cohen
... level, but still not as intimidating as in Ref.[4]. A major issue was to avoid the over emphasis on spherical geometry. The language that I use is much more suitable for research with “mesoscopic” orientation. Some highlights for those who look for original or advanced pedagogical pieces: The EPR pa ...
... level, but still not as intimidating as in Ref.[4]. A major issue was to avoid the over emphasis on spherical geometry. The language that I use is much more suitable for research with “mesoscopic” orientation. Some highlights for those who look for original or advanced pedagogical pieces: The EPR pa ...
Exponential Decay of Quantum Wave Functions
... [4] found pointwise isotropic bounds but his result was not optimal and restricted to Coulomb systems since he used the explicit |r|−1 form. All these results, except Ahlrichs, obtained L2 –decay. In three papers [37, 38, 39], I looked at getting pointwise bounds. In the first paper, I obtained opti ...
... [4] found pointwise isotropic bounds but his result was not optimal and restricted to Coulomb systems since he used the explicit |r|−1 form. All these results, except Ahlrichs, obtained L2 –decay. In three papers [37, 38, 39], I looked at getting pointwise bounds. In the first paper, I obtained opti ...
Ground-state properties of sub-Ohmic spin
... corresponding overlap in Eq. (12) vanishes or not. We are now in a position to lay out a picture of the phase transition, which will be verified by numerical simulations to come. For ε = = 0 there is a phase transition that for a given α occurs at β = βc (α), so that for β < βc the system is in a ...
... corresponding overlap in Eq. (12) vanishes or not. We are now in a position to lay out a picture of the phase transition, which will be verified by numerical simulations to come. For ε = = 0 there is a phase transition that for a given α occurs at β = βc (α), so that for β < βc the system is in a ...
master equation for state occupancies of an open quantum system 121
... the CQS. Transitions between the ath and the bth states are associated with the off-diagonal transfer operator V . To generalize a situation, we suppose that the position of CQS energy levels can be alternated by regular ac-fields or non-regular stochastic fields so that the energy of the ath state ...
... the CQS. Transitions between the ath and the bth states are associated with the off-diagonal transfer operator V . To generalize a situation, we suppose that the position of CQS energy levels can be alternated by regular ac-fields or non-regular stochastic fields so that the energy of the ath state ...
quantum dynamics of integrable spin chains
... The extension to local observables was done in the study of impurity models. Both Tjon [27], and Abraham, Barouch, Gallavotti and Martin-Löf [1, 2, 3] have found the same kind of behavior for the XX model with an impurity. So, definitely, this unusual behavior of such systems could be discouraging, ...
... The extension to local observables was done in the study of impurity models. Both Tjon [27], and Abraham, Barouch, Gallavotti and Martin-Löf [1, 2, 3] have found the same kind of behavior for the XX model with an impurity. So, definitely, this unusual behavior of such systems could be discouraging, ...
DIFFUSION LIMIT OF A GENERALIZED MATRIX
... fields, which can be handled rather easily and more precisely as compared to magnetic fields. In most of the spintronic applications, spin-polarized electron transport in solids plays a crucial role. By spin-polarized transport we mean that, in addition to the charge distribution of an electron syst ...
... fields, which can be handled rather easily and more precisely as compared to magnetic fields. In most of the spintronic applications, spin-polarized electron transport in solids plays a crucial role. By spin-polarized transport we mean that, in addition to the charge distribution of an electron syst ...
CSE 599d - Quantum Computing Introduction and Basics of
... Entscheidungsproblem” where the notion of a universal Turing machine was first introduced. In the years that followed, the optimism of the earlier pioneers in computing must have seemed insane: machines which can execute billions of arithmetic operations per second? Crazy! Even after the invention o ...
... Entscheidungsproblem” where the notion of a universal Turing machine was first introduced. In the years that followed, the optimism of the earlier pioneers in computing must have seemed insane: machines which can execute billions of arithmetic operations per second? Crazy! Even after the invention o ...
Fulltext
... length of b and a height of h capped by composite InGaAs and InAlAs layers were investigated theoretically in a one-band effective mass model framework. It was found that the ground-state emission wavelengths depend not only on the h/b ratio, but also on the thickness and position of the InGaAs and ...
... length of b and a height of h capped by composite InGaAs and InAlAs layers were investigated theoretically in a one-band effective mass model framework. It was found that the ground-state emission wavelengths depend not only on the h/b ratio, but also on the thickness and position of the InGaAs and ...
Wave function
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).For a given system, once a representation corresponding to a maximal set of commuting observables and a suitable coordinate system is chosen, the wave function is a complex-valued function of the system's degrees of freedom corresponding to the chosen representation and coordinate system, continuous as well as discrete. Such a set of observables, by a postulate of quantum mechanics, are Hermitian linear operators on the space of states representing a set of physical observables, like position, momentum and spin that can, in principle, be simultaneously measured with arbitrary precision. Wave functions can be added together and multiplied by complex numbers to form new wave functions, and hence are elements of a vector space. This is the superposition principle of quantum mechanics. This vector space is endowed with an inner product such that it is a complete metric topological space with respect to the metric induced by the inner product. In this way the set of wave functions for a system form a function space that is a Hilbert space. The inner product is a measure of the overlap between physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The actual space depends on the system's degrees of freedom (hence on the chosen representation and coordinate system) and the exact form of the Hamiltonian entering the equation governing the dynamical behavior. In the non-relativistic case, disregarding spin, this is the Schrödinger equation.The Schrödinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name ""wave function"", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical ""space"", and in this respect it differs fundamentally from water waves or waves on a string.For a given system, the choice of which relevant degrees of freedom to use are not unique, and correspondingly the domain of the wave function is not unique. It may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. These descriptions are the most important, but they are not the only possibilities. Just like in classical mechanics, canonical transformations may be used in the description of a quantum system. Some particles, like electrons and photons, have nonzero spin, and the wave function must include this fundamental property as an intrinsic discrete degree of freedom. In general, for a particle with half-integer spin the wave function is a spinor, for a particle with integer spin the wave function is a tensor. Particles with spin zero are called scalar particles, those with spin 1 vector particles, and more generally for higher integer spin, tensor particles. The terminology derives from how the wave functions transform under a rotation of the coordinate system. No elementary particle with spin 3⁄2 or higher is known, except for the hypothesized spin 2 graviton. Other discrete variables can be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).In the Copenhagen interpretation, an interpretation of quantum mechanics, the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place at a given time or having a definite momentum, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.The unit of measurement for ψ depends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.