Is Quantum Mechanics necessary for understanding
... In the macroscopic limit QM typically reduces to classical mechanics, i.e., give similar predictions to those of Newton’s and Maxwell’s equations (macroscopic quantum phenomena exist, but they are few or non-obvious). Luckily the consequence in the context of MR is that a classical description is ad ...
... In the macroscopic limit QM typically reduces to classical mechanics, i.e., give similar predictions to those of Newton’s and Maxwell’s equations (macroscopic quantum phenomena exist, but they are few or non-obvious). Luckily the consequence in the context of MR is that a classical description is ad ...
Ice, spin ice and spin liquids lecture April 16, 2013
... It would thus appear that we are done, having explained both significant facts about spin ice. However, this is not the case. First, the nearest-neighbor Ising antiferromagnet is not so simple after all; in fact, it exhibits a divergent correlation length as T ! 0, which cuts off algebraic, dipolar ...
... It would thus appear that we are done, having explained both significant facts about spin ice. However, this is not the case. First, the nearest-neighbor Ising antiferromagnet is not so simple after all; in fact, it exhibits a divergent correlation length as T ! 0, which cuts off algebraic, dipolar ...
The density matrix renormalization group
... spectrum”), which are related to the Schmidt coefficients: • If the coefficients decay very fast (exponentially, for instance), then we introduce very little error by discarding the smaller ones. • Few coefficients mean less entanglement. In the extreme case of a single non-zero coefficient, the wav ...
... spectrum”), which are related to the Schmidt coefficients: • If the coefficients decay very fast (exponentially, for instance), then we introduce very little error by discarding the smaller ones. • Few coefficients mean less entanglement. In the extreme case of a single non-zero coefficient, the wav ...
76, 023605 (2007).
... interacting spin models which to date have been only approximately or indirectly observed in nature or remain as rather deep but unobserved mathematical constructs. Three exciting possibilities are currently the subject of active study 关5兴. The first 共and the most direct兲 envisions simulation of con ...
... interacting spin models which to date have been only approximately or indirectly observed in nature or remain as rather deep but unobserved mathematical constructs. Three exciting possibilities are currently the subject of active study 关5兴. The first 共and the most direct兲 envisions simulation of con ...
Lecture 4. Macrostates and Microstates (Ch. 2 )
... Each of the microstates is characterized by N numbers, the number of equally probable microstates – 2N, the probability to be in a particular microstate – 1/2N. For a two-state paramagnet in zero field, the energy of all macrostates is the same (0). A macrostate is specified by (N, N). Its multipli ...
... Each of the microstates is characterized by N numbers, the number of equally probable microstates – 2N, the probability to be in a particular microstate – 1/2N. For a two-state paramagnet in zero field, the energy of all macrostates is the same (0). A macrostate is specified by (N, N). Its multipli ...
Lecture 4. Macrostates and Microstates (Ch. 2 )
... Note that the assumption that a system is isolated is important. If a system is coupled to a heat reservoir and is able to exchange energy, in order to replace the system’s trajectory by an ensemble, we must determine the relative occurrence of states with different energies. For example, an ensembl ...
... Note that the assumption that a system is isolated is important. If a system is coupled to a heat reservoir and is able to exchange energy, in order to replace the system’s trajectory by an ensemble, we must determine the relative occurrence of states with different energies. For example, an ensembl ...
Quantum mechanical spin - Theory of Condensed Matter
... Consider a frame of reference which is itself rotating with angular velocity ω about êz . If we impose a magnetic field B0 = B0 êz , in the rotating frame, the observed precession frequency is ω r = −γ(B0 + ω/γ), i.e. an effective field Br = B0 + ω/γ acts in rotating frame. If frame rotates exactl ...
... Consider a frame of reference which is itself rotating with angular velocity ω about êz . If we impose a magnetic field B0 = B0 êz , in the rotating frame, the observed precession frequency is ω r = −γ(B0 + ω/γ), i.e. an effective field Br = B0 + ω/γ acts in rotating frame. If frame rotates exactl ...
Chemical Physics High-spin-low-spin transitions in Fe(II) complexes
... energies are small and the whole picture remains consistent. In the case of TMC the relaxation energies can reach values from 10 to 20 eV when the levels with some significant contribution from d-orbitals are involved [6]. This suggests that the real behavior of delectrons in TMC does not fit the pi ...
... energies are small and the whole picture remains consistent. In the case of TMC the relaxation energies can reach values from 10 to 20 eV when the levels with some significant contribution from d-orbitals are involved [6]. This suggests that the real behavior of delectrons in TMC does not fit the pi ...
Approach to equilibrium of a nondegenerate quantum system: decay
... Abstract. The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effect ...
... Abstract. The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effect ...
Field-theoretic Methods
... A macroscopic density corresponding to an extensive variable that captures the symmetry and thereby characterizes the ordered state of a thermodynamic phase in thermal equilibrium. Nonequilibrium generalizations typically address appropriate stationary values in the long-time limit. ...
... A macroscopic density corresponding to an extensive variable that captures the symmetry and thereby characterizes the ordered state of a thermodynamic phase in thermal equilibrium. Nonequilibrium generalizations typically address appropriate stationary values in the long-time limit. ...
On the Theory of Generalized Algebraic Transformations
... brought a considerable insight into deficiencies of some approximative methods, which mostly fail in predicting correct behaviour near a critical region. In this regard, one of the most essential questions to deal with in the statistical mechanics of exactly solvable models is always to find a preci ...
... brought a considerable insight into deficiencies of some approximative methods, which mostly fail in predicting correct behaviour near a critical region. In this regard, one of the most essential questions to deal with in the statistical mechanics of exactly solvable models is always to find a preci ...
![arXiv:0803.3834v2 [quant-ph] 26 May 2009](http://s1.studyres.com/store/data/015940141_1-1e8e53e4d619ce68a74ed7b6b3742d1d-300x300.png)
arXiv:0803.3834v2 [quant-ph] 26 May 2009
... for new students. The quantum description of angular momentum involves differential operators or new algebra rules that seem to be disconnected from the classical intuition. For small values of angular momentum one needs a quantum description because the quantum fluctuations are as big as the angula ...
... for new students. The quantum description of angular momentum involves differential operators or new algebra rules that seem to be disconnected from the classical intuition. For small values of angular momentum one needs a quantum description because the quantum fluctuations are as big as the angula ...
Finite-temperature mutual information in a simple phase transition
... standard tool to detect the central charge in critical quantum spin chains [2, 3], and the entanglement spectrum in topological insulators is providing a very nice characterization of the spectrum of the corresponding edge modes [4, 5]. Also, second-order quantum phase transitions are characterized ...
... standard tool to detect the central charge in critical quantum spin chains [2, 3], and the entanglement spectrum in topological insulators is providing a very nice characterization of the spectrum of the corresponding edge modes [4, 5]. Also, second-order quantum phase transitions are characterized ...
1.2 The Time–Dependent Schr ¨odinger Equation
... the rate of internal conversion (IC) between an excited electronic state φe and the electronic ground–state φg will be considered as an example; electronic excitation energy is distributed among the different vibrational degrees of freedom; since the radiation field does not take part in this type t ...
... the rate of internal conversion (IC) between an excited electronic state φe and the electronic ground–state φg will be considered as an example; electronic excitation energy is distributed among the different vibrational degrees of freedom; since the radiation field does not take part in this type t ...
Phase Transitions - Helmut Katzgraber
... By a simple argument we can show that in the nearest-neighbour Ising model there is no phase transition in one dimension for non-zero temperature . A phase transition in two dimensions is however possible. Since we are looking for spontaneous magnetization, we set the external magnetic field to zero ...
... By a simple argument we can show that in the nearest-neighbour Ising model there is no phase transition in one dimension for non-zero temperature . A phase transition in two dimensions is however possible. Since we are looking for spontaneous magnetization, we set the external magnetic field to zero ...
A Semi-Classical Approach to the Jaynes
... Separated variables λj are the zeroes B(λj ) = 0. The conjugate variables are µj = −A(λj ). One can reconstruct the Lax matrix itself once we know the coordinates of these n points. For B(λ), we simply have ...
... Separated variables λj are the zeroes B(λj ) = 0. The conjugate variables are µj = −A(λj ). One can reconstruct the Lax matrix itself once we know the coordinates of these n points. For B(λ), we simply have ...
Quantum Relaxation after a Quench in Systems with Boundaries Ferenc Iglo´i *
... and h0 < hc we have AðtÞ cosðat þ bÞ, thus mðtÞ changes sign. On the other hand in the other parts of the phase diagram mðtÞ is always positive, i.e. AðtÞ ½cosðat þ bÞ þ c, with c > 1. The characteristic time scale, ¼ ðh; h0 Þ, is the relaxation or phase coherence time, which is extracted fr ...
... and h0 < hc we have AðtÞ cosðat þ bÞ, thus mðtÞ changes sign. On the other hand in the other parts of the phase diagram mðtÞ is always positive, i.e. AðtÞ ½cosðat þ bÞ þ c, with c > 1. The characteristic time scale, ¼ ðh; h0 Þ, is the relaxation or phase coherence time, which is extracted fr ...
Isometric and unitary phase operators: explaining the Villain transform
... of elementary excitations in a system of extensively many Heisenberg spins. Intuitively, it is a representation of the spin operators in terms of an angle and its canonically conjugate angular momentum operator and, as such, has a few nasty boundary-condition twists. We construct an isometric phase ...
... of elementary excitations in a system of extensively many Heisenberg spins. Intuitively, it is a representation of the spin operators in terms of an angle and its canonically conjugate angular momentum operator and, as such, has a few nasty boundary-condition twists. We construct an isometric phase ...
Ph. D. thesis Quantum Phase Transitions in Correlated Systems
... transitions are associated with the singularities of thermodynamic quantities and, accordingly, can be traditionally classified as first-order or second-order transitions. In experiments, control parameters can be temperature, pressure, magnetic and electric fields or doping. When the phase transiti ...
... transitions are associated with the singularities of thermodynamic quantities and, accordingly, can be traditionally classified as first-order or second-order transitions. In experiments, control parameters can be temperature, pressure, magnetic and electric fields or doping. When the phase transiti ...
Prof. Darrick Chang - Lecures - ICFO Schools on the Frontiers of Light
... • Motion should be initially cold (ground state, quantum degenerate) • Motional time scales are very slow (atoms scatter many photons) • Scattering leads to recoil heating and breaks spin correlations ...
... • Motion should be initially cold (ground state, quantum degenerate) • Motional time scales are very slow (atoms scatter many photons) • Scattering leads to recoil heating and breaks spin correlations ...
Decoherence and quantum quench: their relationship with excited
... A QQ represents an abrupt, diabatic change λ1 → λ2 of the control parameter followed by a system-specific quantum relaxation process. Pioneering theoretical works in this field appeared already in the late 1960s [3], but a really rapid growth of interest was triggered by experimental studies at the ...
... A QQ represents an abrupt, diabatic change λ1 → λ2 of the control parameter followed by a system-specific quantum relaxation process. Pioneering theoretical works in this field appeared already in the late 1960s [3], but a really rapid growth of interest was triggered by experimental studies at the ...
Low-energy fixed points of random Heisenberg models Y.-C. Lin R. Me´lin
... that are arbitrarily far from each other. Fisher’s SDRG treatment has been extended to the dimerized phases that turned out to be equivalent to quantum Griffiths phases.8 The SDRG method has also been applied for random S⫽1 共Ref. 9兲 and S⫽3/2 共Ref. 10兲 spin chains and for various random spin ladder ...
... that are arbitrarily far from each other. Fisher’s SDRG treatment has been extended to the dimerized phases that turned out to be equivalent to quantum Griffiths phases.8 The SDRG method has also been applied for random S⫽1 共Ref. 9兲 and S⫽3/2 共Ref. 10兲 spin chains and for various random spin ladder ...
