Quantum anomalous Hall effect with cold atoms trapped in a square
... M = 0, since the edge states are localized on the boundaries, we may consider two basic situations for the Bragg scattering: First, we shine the two lasers on one boundary (on x = 0 or x = L) of the system; second, we shine them on the whole lattice system including both boundaries. For the former c ...
... M = 0, since the edge states are localized on the boundaries, we may consider two basic situations for the Bragg scattering: First, we shine the two lasers on one boundary (on x = 0 or x = L) of the system; second, we shine them on the whole lattice system including both boundaries. For the former c ...
Chapter 4 The Statistical Physics of non
... We will see later all thermodynamic quantities (E, S, F, P etc.) can be determined via the partition function Z. So it is important to learn how to calculate the partition function. In general, calculation of partition function of a thermodynamic system is complicated due to the interactions between ...
... We will see later all thermodynamic quantities (E, S, F, P etc.) can be determined via the partition function Z. So it is important to learn how to calculate the partition function. In general, calculation of partition function of a thermodynamic system is complicated due to the interactions between ...
The rotation of a homonuclear linear molecule
... The parities of the rotational wave functions (their symmetries with respect to inversion) alternate odd and even with successive J. That means that the energy levels correspond to even rotational states for even J and to odd states for odd J. We shall see the significance of this remark about the p ...
... The parities of the rotational wave functions (their symmetries with respect to inversion) alternate odd and even with successive J. That means that the energy levels correspond to even rotational states for even J and to odd states for odd J. We shall see the significance of this remark about the p ...
Folds, Bosonization and non-triviality of the classical limit of 2D
... im (x, t) − 1 denotes the number of “folds” at the point x at time t. In the absence of folds, one can set β+ (x, t) = p1 (x, t) and β− (x, t) = q1 (x, t) which then implies that all the w±,n = 0. This is the standard bosonization in terms of the collective field theory. As emphasized in [4] and [5 ...
... im (x, t) − 1 denotes the number of “folds” at the point x at time t. In the absence of folds, one can set β+ (x, t) = p1 (x, t) and β− (x, t) = q1 (x, t) which then implies that all the w±,n = 0. This is the standard bosonization in terms of the collective field theory. As emphasized in [4] and [5 ...
Magnetic ordering of nuclear spins in an interacting two-dimensional electron... Pascal Simon, Bernd Braunecker, and Daniel Loss
... that the SW transformation neglects retardation effects. This is appropriate since the the nuclear spin dynamics is slow compared to the electron one 共in terms of energy scales, this is related to the fact that A Ⰶ EF兲. Therefore, electrons see an almost static nuclear spin background, and the adiab ...
... that the SW transformation neglects retardation effects. This is appropriate since the the nuclear spin dynamics is slow compared to the electron one 共in terms of energy scales, this is related to the fact that A Ⰶ EF兲. Therefore, electrons see an almost static nuclear spin background, and the adiab ...
Diamagnetism and de Haas-van Alphen oscillations in the electronic
... de Haas-van Alphen (dHvA) effect (§1.2). We are interested in deriving magnetic quantities, as susceptibility, from theoretical considerations. This theory will be done after a presentation of the single-particle Hamiltonian that governs the energy of free, noninteracting electrons in an external ma ...
... de Haas-van Alphen (dHvA) effect (§1.2). We are interested in deriving magnetic quantities, as susceptibility, from theoretical considerations. This theory will be done after a presentation of the single-particle Hamiltonian that governs the energy of free, noninteracting electrons in an external ma ...
Aharonov–Bohm interferometry with the T-shaped capacitively coupled quantum dots
... For different fluxes φ1 ≠ φ2, the orbital degeneracy is broken. Figure 1b (φ1/φ2 = 1/4) presents an example of the two-period oscillations of conductance and Fig. 1c illustrates the Coulomb induced AB oscillations (oscillations observed also in the ring, where no magnetic flux is applied, φ2 = 0). F ...
... For different fluxes φ1 ≠ φ2, the orbital degeneracy is broken. Figure 1b (φ1/φ2 = 1/4) presents an example of the two-period oscillations of conductance and Fig. 1c illustrates the Coulomb induced AB oscillations (oscillations observed also in the ring, where no magnetic flux is applied, φ2 = 0). F ...
Unified rotational and permutational symmetry and selection rules in
... rows have λ1≥λ2≥...≥λp boxes ...
... rows have λ1≥λ2≥...≥λp boxes ...
Lecture 1 Review of hydrogen atom Heavy proton (put at the origin
... Spin of elementary particles has nothing to do with rotation, does not depend on coordinates and , and is purely a quantum mechanical phenomena. ...
... Spin of elementary particles has nothing to do with rotation, does not depend on coordinates and , and is purely a quantum mechanical phenomena. ...
Nature template - PC Word 97
... the superfluid density. The two values are in fair agreement, but we note that the exact relation between ρC and ρS in 2D atomic gases will require further experimental and theoretical investigation. For example, our observation of ~ 0.5 for a finite value of c0 suggests that the superfluid densit ...
... the superfluid density. The two values are in fair agreement, but we note that the exact relation between ρC and ρS in 2D atomic gases will require further experimental and theoretical investigation. For example, our observation of ~ 0.5 for a finite value of c0 suggests that the superfluid densit ...
... Quantum dots (QD) are zero dimensional objects constructed by patterning and epitaxial growth techniques in semiconductor heterostructures [1]. An important characteristic of these systems is that the phase coherent length of the electron wave functions exceeds the size of the dots, and consequently ...
Metal Insulator Transition
... There are two most relevant quantities for discussing metal insulator transition in Hubbard model, Drude weight and the charge compressibility. ...
... There are two most relevant quantities for discussing metal insulator transition in Hubbard model, Drude weight and the charge compressibility. ...
Spin Hamiltonians and Exchange interactions
... This term looks anisotropic in that H defines a special direction in space. 3 But the material is isotropic in spin space, in the sense that the strength of its field coupling is independent of the field’s direction. P It’s convenient to rewrite HH = −H · i Si , absorbing the gµB coefficient into th ...
... This term looks anisotropic in that H defines a special direction in space. 3 But the material is isotropic in spin space, in the sense that the strength of its field coupling is independent of the field’s direction. P It’s convenient to rewrite HH = −H · i Si , absorbing the gµB coefficient into th ...
Statistical Methods and Thermodynamics Chem 530b: Lecture
... |ψ >. Note that such collection of N replica systems is also described by a pure state. Therefore, the ensemble averages associated with the observables ô and  of such a pure state will coincide with the expectation values given by the equations Eq. (5) and Eq. (6), respectively. ...
... |ψ >. Note that such collection of N replica systems is also described by a pure state. Therefore, the ensemble averages associated with the observables ô and  of such a pure state will coincide with the expectation values given by the equations Eq. (5) and Eq. (6), respectively. ...
THE CASIMIR EFFECT
... connected to the ground state, by off-diagonal matrix elements of the dipole moments d~1 = ~ri or P d~2 = ~rj . For atoms with J = 0 ground states, i.e. with spherical shapes, the sum in Eq. 32 is limited to J = 1 states, but involves a summation over the magnetic quantum numbers. Using the Wigner-E ...
... connected to the ground state, by off-diagonal matrix elements of the dipole moments d~1 = ~ri or P d~2 = ~rj . For atoms with J = 0 ground states, i.e. with spherical shapes, the sum in Eq. 32 is limited to J = 1 states, but involves a summation over the magnetic quantum numbers. Using the Wigner-E ...
high-temperature superconductivity from short
... is that since fermions are in antisymmetric states, a sign (±) has to be attached to each Monte Carlo configuration. That prevents the sampling to be efficient at low temperatures in many cases. Nevertheless, there are some non-trivial regimes where Monte Carlo can be used as a benchmark for TPSC [1 ...
... is that since fermions are in antisymmetric states, a sign (±) has to be attached to each Monte Carlo configuration. That prevents the sampling to be efficient at low temperatures in many cases. Nevertheless, there are some non-trivial regimes where Monte Carlo can be used as a benchmark for TPSC [1 ...
chapter link
... fragments and the diffusion lifetime. Both the conservation of angular momentum and the conservation of energy must be satisfied and this leads to the selection rules for the allowed transitions. Under the conditions shown in Figure 5 the allowed transitions are for the S to all T states and between ...
... fragments and the diffusion lifetime. Both the conservation of angular momentum and the conservation of energy must be satisfied and this leads to the selection rules for the allowed transitions. Under the conditions shown in Figure 5 the allowed transitions are for the S to all T states and between ...
Theoretical Statistical Physics
... 10.2.4. Critical exponent of correlation length and anomalous dimension 10.2.5. Critical opalescence . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1. Macroscopic laws for second order phase transition . . ...
... 10.2.4. Critical exponent of correlation length and anomalous dimension 10.2.5. Critical opalescence . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1. Macroscopic laws for second order phase transition . . ...
PPT - Fernando Brandao
... Gives first polynomial-time quantum algorithm for preparing Gibbs states of commuting models at high temperature. Caveat: At high temperature cluster expansion works well for computing local expectation values. (Open: How the two threshold T’s compare?) Q advantage: we get the full Gibbs state (e.g. ...
... Gives first polynomial-time quantum algorithm for preparing Gibbs states of commuting models at high temperature. Caveat: At high temperature cluster expansion works well for computing local expectation values. (Open: How the two threshold T’s compare?) Q advantage: we get the full Gibbs state (e.g. ...
Electron energy level statistics in graphene quantum dots
... the interval [t – δ, t + δ] and/or we add on-site potentials vi and vj in the range [–v, v]. The geometrical shape “cuts out” a piece of the hexagonal lattice such that armchair and zigzag parts of the boundary appear (for a general discussion of boundary conditions for the tight-binding model of gr ...
... the interval [t – δ, t + δ] and/or we add on-site potentials vi and vj in the range [–v, v]. The geometrical shape “cuts out” a piece of the hexagonal lattice such that armchair and zigzag parts of the boundary appear (for a general discussion of boundary conditions for the tight-binding model of gr ...
Negative energy densities in integrable quantum field theories at
... In the present paper, we will investigate the inequality (1.1) in a specific class of self-interacting models on 1+1 dimensional Minkowski space, so-called quantum integrable models, which have recently become amenable to a rigorous construction. Specifically, we consider integrable models with one ...
... In the present paper, we will investigate the inequality (1.1) in a specific class of self-interacting models on 1+1 dimensional Minkowski space, so-called quantum integrable models, which have recently become amenable to a rigorous construction. Specifically, we consider integrable models with one ...