Localization and the Integer Quantum Hall effect
... Figure 1.2.1: Anderson localization in d = 3: (a). schematic density of states, showing the mobility edge between extended and localized states. (This picture corresponds to t ∼ W , and the bandwidth is of the same order.) (b). critical divergence of localization length, as a function of eigenstate ...
... Figure 1.2.1: Anderson localization in d = 3: (a). schematic density of states, showing the mobility edge between extended and localized states. (This picture corresponds to t ∼ W , and the bandwidth is of the same order.) (b). critical divergence of localization length, as a function of eigenstate ...
Heat diffusion from the more general perspective and its application
... magnon-phonon interaction. We are trying now to find a better mathematical expression for the contribution of magnetoelastic energy in the special materials. In connection with it appears to us as promising an exploitation of hypercomplex mathematics. We turned our attention, for example, to the ind ...
... magnon-phonon interaction. We are trying now to find a better mathematical expression for the contribution of magnetoelastic energy in the special materials. In connection with it appears to us as promising an exploitation of hypercomplex mathematics. We turned our attention, for example, to the ind ...
Quantum Hall effect
... spin/valley degeneracy, which we have not talked about. condition, Eq.(5), lifts the K, K ′ dege This leads to additional integer states at numbers of edge modes lead to the hal higher fields. split graphene edge states: the blue the spin up (spin down) states. Th ...
... spin/valley degeneracy, which we have not talked about. condition, Eq.(5), lifts the K, K ′ dege This leads to additional integer states at numbers of edge modes lead to the hal higher fields. split graphene edge states: the blue the spin up (spin down) states. Th ...
1 III Equilibrium statistical mechanics (Hiroshi Matsuoka) The goal
... As discussed above, f is a decreasing convex or bowed-down function of v. As we will see later in the next chapter, this expression for the Helmholtz free energy is based on an approximation that the temperature of the gas is not too low so that we do not need to take into account whether the atoms ...
... As discussed above, f is a decreasing convex or bowed-down function of v. As we will see later in the next chapter, this expression for the Helmholtz free energy is based on an approximation that the temperature of the gas is not too low so that we do not need to take into account whether the atoms ...
Direct Measurement of Topological Numbers with
... where Ec and σ are the fit center and the fit error of the energy spectrum [see Fig. 3(d)]. Figure 4(b) gives a clear illustration of the topological phase transition by measuring ν versus μ, where a sharp change of ν occurs near μ ≈ −1.3. The deviation of the critical point from the theoretical exp ...
... where Ec and σ are the fit center and the fit error of the energy spectrum [see Fig. 3(d)]. Figure 4(b) gives a clear illustration of the topological phase transition by measuring ν versus μ, where a sharp change of ν occurs near μ ≈ −1.3. The deviation of the critical point from the theoretical exp ...
Enhanced and Reduced Atom Number
... originate from the interplay between interactions and quantum statistics. Lowering the temperature, the onset of superbinomial fluctuations occurs when quantum degeneracy becomes important. Fluctuations are given by the probability distribution of the macroscopic configurations with a given atom num ...
... originate from the interplay between interactions and quantum statistics. Lowering the temperature, the onset of superbinomial fluctuations occurs when quantum degeneracy becomes important. Fluctuations are given by the probability distribution of the macroscopic configurations with a given atom num ...
Quantum mechanical spin and addition of angular momenta
... Until we have focussed on the quantum mechanics of particles which are “featureless”, carrying no internal degrees of freedom. However, a relativistic formulation of quantum mechanics shows that particles can exhibit an intrinsic angular momentum component known as spin. However, the discovery of th ...
... Until we have focussed on the quantum mechanics of particles which are “featureless”, carrying no internal degrees of freedom. However, a relativistic formulation of quantum mechanics shows that particles can exhibit an intrinsic angular momentum component known as spin. However, the discovery of th ...
Disorder(Strength(δ2( Energy( Density( Ext,(( Para( ( MBL( Para
... the ground state, of MBL systems and point out that they come in many flavors, and may be classified in terms of broken symmetries, topological order and/or criticality, very much as in the usual account of phases and phase transitions in equilibrium systems. We note that in the presence of many-bod ...
... the ground state, of MBL systems and point out that they come in many flavors, and may be classified in terms of broken symmetries, topological order and/or criticality, very much as in the usual account of phases and phase transitions in equilibrium systems. We note that in the presence of many-bod ...
Detection of Quantum Critical Points by a Probe Qubit
... Discussion and conclusion.—In conclusion, we have shown that a probe qubit can be used to detect quantum critical points. It is first placed into a superposition state and then coupled to the system undergoing the QPT. When the two eigenstates become correlated to two different phases, the superposi ...
... Discussion and conclusion.—In conclusion, we have shown that a probe qubit can be used to detect quantum critical points. It is first placed into a superposition state and then coupled to the system undergoing the QPT. When the two eigenstates become correlated to two different phases, the superposi ...
Chapter 10
... The magnitude of the spin (intrinsic angular momentum) for an an electon is ~/2, and so the spin operators are the Pauli operators scaled by ~/2: Sˆx = ~/2 x , Sˆy = ~/2 y , Sˆz = ~/2 z . These spin operators will play a central role in our study of spin. Let us now step back and consider what we ha ...
... The magnitude of the spin (intrinsic angular momentum) for an an electon is ~/2, and so the spin operators are the Pauli operators scaled by ~/2: Sˆx = ~/2 x , Sˆy = ~/2 y , Sˆz = ~/2 z . These spin operators will play a central role in our study of spin. Let us now step back and consider what we ha ...
The Interaction of Radiation and Matter: Quantum
... -- we can identify the significance of a light source's degree of first-order temporal coherence and demonstrate how that coherence can be measured. Consider the following basic experimental configuration: ...
... -- we can identify the significance of a light source's degree of first-order temporal coherence and demonstrate how that coherence can be measured. Consider the following basic experimental configuration: ...
1 Correlated Electrons: Why we need Models to - cond
... single-particle excitation spectrum as well as the k-dependence of the spectral function, and we restrict ourselves to only the ground state energy of the many-electron system. Moreover, we also lose information about all collective excitations in solids, such as plasmons or magnons, which can be ob ...
... single-particle excitation spectrum as well as the k-dependence of the spectral function, and we restrict ourselves to only the ground state energy of the many-electron system. Moreover, we also lose information about all collective excitations in solids, such as plasmons or magnons, which can be ob ...
Spontaneous Dimensional Reduction in Quantum Gravity
... To even pose the question of dimensional reduction, we must think carefully about the term “dimension.” In general relativity, spacetime is modeled as a smooth manifold, and dimension is unambiguous. Kaluza-Klein theory uses higher-dimensional manifolds, again with no real ambiguity. But quantum gra ...
... To even pose the question of dimensional reduction, we must think carefully about the term “dimension.” In general relativity, spacetime is modeled as a smooth manifold, and dimension is unambiguous. Kaluza-Klein theory uses higher-dimensional manifolds, again with no real ambiguity. But quantum gra ...
IOSR Journal of Applied Physics (IOSR-JAP)
... spin polarization can be achieved either through an equilibrium energy splitting between spin up and spin down such as putting a material in a large magnetic field (Zeeman effect) or the exchange energy present in a ferromagnet, or forcing the system out of equilibrium. We focus on the case when the ...
... spin polarization can be achieved either through an equilibrium energy splitting between spin up and spin down such as putting a material in a large magnetic field (Zeeman effect) or the exchange energy present in a ferromagnet, or forcing the system out of equilibrium. We focus on the case when the ...
Spin filters with Fano dots - the Max Planck Institute for the Physics
... comprehensive picture of a big variety of underlying physical phenomena has emerged (See e.g. [4, 5] and references therein). Confinement of electrons in small quantum dots leads to the necessity of taking into account their Coulomb repulsion. At finite temperatures the main effect is the Coulomb bl ...
... comprehensive picture of a big variety of underlying physical phenomena has emerged (See e.g. [4, 5] and references therein). Confinement of electrons in small quantum dots leads to the necessity of taking into account their Coulomb repulsion. At finite temperatures the main effect is the Coulomb bl ...
Vortex states of a disordered quantum Hall bilayer P. R. Eastham,
... our unit of energy. Thus Gij = V共rij兲 − V共0兲 is the lattice solution to ⵜ2V共r兲 = −2␦共0兲, with the singularity removed.19 Ground states were obtained by simulated annealing, with standard nearest-neighbor Monte Carlo moves. Each ground state is obtained by recording the lowest energy state obtained ...
... our unit of energy. Thus Gij = V共rij兲 − V共0兲 is the lattice solution to ⵜ2V共r兲 = −2␦共0兲, with the singularity removed.19 Ground states were obtained by simulated annealing, with standard nearest-neighbor Monte Carlo moves. Each ground state is obtained by recording the lowest energy state obtained ...
Infinite-randomness quantum critical points induced by dissipation
... transitions are governed by conventional critical points.21–24 As in the Ising case, adding Ohmic dissipation hampers the dynamics of O共N兲 symmetric order parameters. Vojta and Schmalian25 showed that the “energy gap” of large locally ordered droplets is exponentially small in their volume leading t ...
... transitions are governed by conventional critical points.21–24 As in the Ising case, adding Ohmic dissipation hampers the dynamics of O共N兲 symmetric order parameters. Vojta and Schmalian25 showed that the “energy gap” of large locally ordered droplets is exponentially small in their volume leading t ...