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Electron spin and probability current density in quantum mechanics
Electron spin and probability current density in quantum mechanics

... momentum for an arbitrary spinor state W. From that he identifies a spin probability current density. His result is the same as our Eq. (32), except that it does not include the g-factor. His paper has a discussion of why that might be appropriate. Nowakowski obtains Eq. (32) by starting from the re ...
Effective-field theory on the transverse Ising model under a time
Effective-field theory on the transverse Ising model under a time

92, 054101 (2004)
92, 054101 (2004)

... strength, i.e., gc  1:96, above which the mean number of noncondensed atoms increases exponentially, indicating the instability of BEC. Below the critical point, the mean number of noncondensed atoms increases polynomially. As the nonlinear parameter crosses over the critical point, the growth rate ...
Hubbard and Kondo lattice models in two dimensions: A QMC study
Hubbard and Kondo lattice models in two dimensions: A QMC study

... that (i) the local screening of impurity spins determines the low-energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the half-filled Hubbard model at J = 0 to that of the Kondo insulator at J > Jc . Our results are based on both T = 0 Quantum Mo ...
Homework # 4
Homework # 4

Quantum relaxation and finite-size effects in the XY chain in... transverse field after global quenches
Quantum relaxation and finite-size effects in the XY chain in... transverse field after global quenches

... the SC theory. We observe an excellent agreement for short times before the first maximum, where the first QP that have undergone a reflection at a boundary reach the middle of the chain. Small deviations are caused by these reflections and accumulate in the subsequent periods. In the SC calculation one ...
Quantum spin systems from the perspective of quantum
Quantum spin systems from the perspective of quantum

... 2 possible methods to sum this: -If N!1 and homogeneous, one can calculate the largest eigenvector of a column transfer matrix (TMRG) using DMRG with PERIODIC boundary condition (note that it is not always possible to get hermitean transfer matrices) ...
N - Princeton University
N - Princeton University

... The significance of this result is that it must be a purely intrabasin vibrational phenomenon. In this low temperature limit, the system resides exclusively in one of the permutationequivalent basins for the perfect BCC crystal. While the isochoric inherent structures for the fluid phase above T*mp( ...
Optically polarized atoms_ch_2
Optically polarized atoms_ch_2

... Projections of li are not conserved, but the total orbital momentum L is, along with its projection ! This is because li form sort of an isolated system So far, we have been ignoring spins One might think that since we have neglected (ls) interaction, energies of states do not depend on spins ...
The Quantum Theory of the Emission and Absorption of Radiation
The Quantum Theory of the Emission and Absorption of Radiation

... in which it can be applied to systems for which the Hamiltonian involves the time explicitly. One may have a dynamical system specified by a Hamiltonian H which cannot be expressed as an algebraic function of any set of canonical variables, but which can all the same be represented by a matrix H(ξ 0 ...
Integrable Systems: An Overview Preamble. The following pages
Integrable Systems: An Overview Preamble. The following pages

Partition function (statistical mechanics)
Partition function (statistical mechanics)

Appendix-Revised_FINAL
Appendix-Revised_FINAL

+1/2 - WordPress.com
+1/2 - WordPress.com

... Number of spin states or multiplicity: If we place an magnetically active nucleus in an external magnetic field, how many orientations it can adopt. Number of spin states is given by formula: m = 2I + 1 For example, for a nucleus with I = ½, m=2*½+1=2 So it has two spin states (or, orientations, or ...
Lecture 8: The fractional quantum Hall effect The fractional quantum
Lecture 8: The fractional quantum Hall effect The fractional quantum

... we will see that in a sense a nonzero compressibility is realized there. We are now in a position to answer our original question, namely, what happens when, in a Corbino-disk geometry, we adiabatically increase the AB flux by one flux quantum? The first point to make is that after such an increase ...
PHONON I: The dispersion relation (by CHY) Introduction The static
PHONON I: The dispersion relation (by CHY) Introduction The static

... 2C/Mlighter for the optical branch. (Mheavier is the mass of the heavier one between M1 and M2 .) Homework: Find the phonon energies for Si, Ge, and GaAs, and Calculate the size of their first B.Z. Plot their phonon dispersion relations. For the same k, optical phonon energy is higher than the corre ...
Quantum Spin Hall Effect and Enhanced Magnetic Response by
Quantum Spin Hall Effect and Enhanced Magnetic Response by

... phases depending on whether N is even or odd. To observe the QSH phase experimentally, one way is to measure the spin current by an applied electric field. We note that the QSH phase does not show a quantization [6], unlike the quantum Hall effect (QHE). On the other hand, surprisingly, the critical ...
Fulltext PDF
Fulltext PDF

... or mentally - around things made with round lines. But we are in a straitjacket, having to accept one or the other, when often some intermediate form would be better. To draw something freehand such as the patchwork traffic circle they tried in Stockholm - will not do. It isn't fixed, isn't definite ...
Kronig–Penney Model
Kronig–Penney Model

... diminishes. This also leads to increase of the distance between electrons and the total energy possessed by the individual electron. 3.Conversly if suppose the effect of potential barrier dominate i.e., if P is large, the resultant wave obtained in terms of shows a stepper variation in the region li ...
Document
Document

Probability - Mr. Taylor`s Math
Probability - Mr. Taylor`s Math

... defectives. The manager in the store receives a new shipment of microcomputers and discovers that 40% are from factory C, 40% are from factory B, and 20% are from factory A. (Hint: make a tree diagram) a) What is the probabilities of finding a defective microcomputer in this shipment? b) Are the eve ...
Chapter 12 What is a paramagnetic material?
Chapter 12 What is a paramagnetic material?

... They are weakly attracted to a magnetic field. ...
Haldane charge conjecture in one-dimensional
Haldane charge conjecture in one-dimensional

... is doped by non-magnetic impurities.3 The possibility of a similar hidden order has recently been proposed in a different context, by studying the one-dimensional extended BoseHubbard model.4 In this Rapid Communication, we will reveal a Haldane conjecture for spin-singlet modes in a 2N -component f ...
Griffiths singularities in the disordered phase of a quantum Ising... H. Rieger
Griffiths singularities in the disordered phase of a quantum Ising... H. Rieger

spin-dependent selection rules for dipole transitions
spin-dependent selection rules for dipole transitions

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Ising model

The Ising model (/ˈaɪsɪŋ/; German: [ˈiːzɪŋ]), named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice, allowing each spin to interact with its neighbors. The model allows the identification of phase transitions, as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition.The Ising model was invented by the physicist Wilhelm Lenz (1920), who gave it as a problem to his student Ernst Ising. The one-dimensional Ising model has no phase transition and was solved by Ising (1925) himself in his 1924 thesis. The two-dimensional square lattice Ising model is much harder, and was given an analytic description much later, by Lars Onsager (1944). It is usually solved by a transfer-matrix method, although there exist different approaches, more related to quantum field theory.In dimensions greater than four, the phase transition of the Ising model is described by mean field theory.
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