Chapter 4: Variable Range Hopping Conduction
... In 1968 Mott introduced the concept of a type of hopping conduction called variable range hopping (vrh) [19]. Although Mott’s original manuscript successfully described the empirically observed log σ ∼ T−1/4 dependence, the derivation of this relation proved rather unsatisfactory from a statistical ...
... In 1968 Mott introduced the concept of a type of hopping conduction called variable range hopping (vrh) [19]. Although Mott’s original manuscript successfully described the empirically observed log σ ∼ T−1/4 dependence, the derivation of this relation proved rather unsatisfactory from a statistical ...
Fluctuations in Ideal and Interacting Bose
... überwunden zu werden” (problems exist to be overcome). This statement holds true not only for scientific matters but also for science policy. Three examples illustrating his qualities offer themselves: In the early 1980s the Max-Planck-Society inherited the Ringberg castle located in the picturesque ...
... überwunden zu werden” (problems exist to be overcome). This statement holds true not only for scientific matters but also for science policy. Three examples illustrating his qualities offer themselves: In the early 1980s the Max-Planck-Society inherited the Ringberg castle located in the picturesque ...
Variations on the adiabatic invariance: the Lorentz pendulum
... Rayleigh’s previous work, raised the question of the behavior of a “quantum pendulum” the length of which is gradually altered3 (by historical vicissitudes4 his name has become inextricably linked to that system). Einstein’s reply was that “if the length of the pendulum is changed infinitely slowly, ...
... Rayleigh’s previous work, raised the question of the behavior of a “quantum pendulum” the length of which is gradually altered3 (by historical vicissitudes4 his name has become inextricably linked to that system). Einstein’s reply was that “if the length of the pendulum is changed infinitely slowly, ...
An n-Dimensional Generalization of the Rhombus Tiling
... the height itself is a vector, giving an surface in four or more dimensions. These include antiferromagnetic Potts models, bond-coloring models, and fully-packed loop models on various lattices [19, 27, 42, 6, 34]. Height-like functions have also been defined which can take a dense set of values in ...
... the height itself is a vector, giving an surface in four or more dimensions. These include antiferromagnetic Potts models, bond-coloring models, and fully-packed loop models on various lattices [19, 27, 42, 6, 34]. Height-like functions have also been defined which can take a dense set of values in ...
Asymptotic analysis and quantum integrable models
... I am also thankful to the administrative staff of the Institut de Mathématiques de Bourgogne. I thank L. Paris, the director, for all his efforts that resulted in an efficient and harmonious functioning of the laboratory. I thank the secretaries, Anissa Bellaassali, Ibtissam Bourtadi, Nadia Bader, Carol ...
... I am also thankful to the administrative staff of the Institut de Mathématiques de Bourgogne. I thank L. Paris, the director, for all his efforts that resulted in an efficient and harmonious functioning of the laboratory. I thank the secretaries, Anissa Bellaassali, Ibtissam Bourtadi, Nadia Bader, Carol ...
Leaking Chaotic Systems
... leak size to zero is assured. Leaking systems can be both dissipative and conservative (Hamiltonian). Within this latter category, we consider the problem of chaotic scattering [as typically defined, e.g., (Gaspard, 1998)] to be beyond the scope of this review because it lacks properties (i) and (ii ...
... leak size to zero is assured. Leaking systems can be both dissipative and conservative (Hamiltonian). Within this latter category, we consider the problem of chaotic scattering [as typically defined, e.g., (Gaspard, 1998)] to be beyond the scope of this review because it lacks properties (i) and (ii ...
Number Fluctuations and Phase Diffusion in a Bose
... are not in true equilibrium, since the steady state is a dynamical balance between particle losses and particle gain by external pumping with a laser. Due to these differences, new experimental possibilities have opened up. For example, large number fluctuations of the order of the total particle nu ...
... are not in true equilibrium, since the steady state is a dynamical balance between particle losses and particle gain by external pumping with a laser. Due to these differences, new experimental possibilities have opened up. For example, large number fluctuations of the order of the total particle nu ...
Special functions in R: introducing the gsl package
... and completely wrapped. Functions are named such that one can identify a function in the GSL manual, and the corresponding R command will be the same but with the prefix1 and, if present, the “_e” suffix, removed. In the case of the special functions, the prefix is “gsl_sf_”. Thus, GSL function gsl_ ...
... and completely wrapped. Functions are named such that one can identify a function in the GSL manual, and the corresponding R command will be the same but with the prefix1 and, if present, the “_e” suffix, removed. In the case of the special functions, the prefix is “gsl_sf_”. Thus, GSL function gsl_ ...
Chap 15 Quantum Physics Physics
... Quantum physics emerged, its wider acceptance was at the Fifth Solvay Conference in 1927. Chap 15 ...
... Quantum physics emerged, its wider acceptance was at the Fifth Solvay Conference in 1927. Chap 15 ...
Theoretical Studies of Ultrafast Correlated Electron
... graduate school would not have been possible. Here, I would like to thank every one who has lent me kind help, support, and encouragement. First of all, I am in heavy debt to my advisor, Prof. Andreas Becker. Doing research is like sailing on the vast ocean, which would not be possible if there is n ...
... graduate school would not have been possible. Here, I would like to thank every one who has lent me kind help, support, and encouragement. First of all, I am in heavy debt to my advisor, Prof. Andreas Becker. Doing research is like sailing on the vast ocean, which would not be possible if there is n ...
Chapter 7 Quantum Error Correction
... The logical basis states |0̄i and |1̄i are eigenstates of these operators with eigenvalue 1. But flipping any of the three qubits changes these eigenvalues. For example, if Z 1 Z 2 = −1 and Z 2Z 3 = 1, then we infer that the first qubit has flipped relative to the other two. We may recover from the ...
... The logical basis states |0̄i and |1̄i are eigenstates of these operators with eigenvalue 1. But flipping any of the three qubits changes these eigenvalues. For example, if Z 1 Z 2 = −1 and Z 2Z 3 = 1, then we infer that the first qubit has flipped relative to the other two. We may recover from the ...
Information Geometric Superactivation of Asymptotic Quantum
... [Shor94], and Grover introduced the quantum searching algorithm in 1996 [Grover96], results in the field of quantum algorithms tapered off somewhat. In the middle of the 90s, there was a silence in the field of quantum algorithms and this did not change until the beginning of the present century. Th ...
... [Shor94], and Grover introduced the quantum searching algorithm in 1996 [Grover96], results in the field of quantum algorithms tapered off somewhat. In the middle of the 90s, there was a silence in the field of quantum algorithms and this did not change until the beginning of the present century. Th ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.