This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Consider the problem of approximately counting weighted independent sets of a graph G with activity λ, i.e., where the weight of an independent set I is λ|I|. We present a novel analysis yielding a deterministic approximation scheme which runs in polynomial time for any graph of maximum degree Δ and λ

/pdf/counting-independent-sets-up-to-the-tree-threshold-2x8fqw89hk.pdf

Counting independent sets up to the tree threshold

Quantum wave packet revivals

Wigner functions and Weyl transforms of operators offer a formulation of quantum mechanics that is equivalent to the standard approach given by the Schrodinger equation. We give a short introduction and emphasize features that give insight into the nature of quantum mechanics and its relation to classical physics. A careful discussion of the classical limit and its difficulties is also given. The discussion is self-contained and includes complete derivations of the results presented.

Wigner functions and Weyl transforms for pedestrians

Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

/pdf/nine-formulations-of-quantum-mechanics-6to57u2wkc.pdf

Nine formulations of quantum mechanics

This paper lists 15 commonly held misconceptions concerning quantum mechanics, such as ‘‘Energy eigenstates are the only allowed states’’ and ‘‘The wave function is dimensionless.’’ A few suggestions are offered to help combat these misconceptions in teaching.

/pdf/common-misconceptions-regarding-quantum-mechanics-3vhcuv1tqa.pdf

Common misconceptions regarding quantum mechanics

What is the qualitative character of entropy? Several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer. The common answer of “entropy as disorder” is regarded here as inadequate. An alternative but equally problematic analogy is “entropy as freedom.” Neither simile is perfect, but if both are used cautiously and not too literally, then the combination provides considerable insight.

Insight into entropy

This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.

/pdf/the-strange-world-of-quantum-mechanics-4mncbvq1j1.pdf

The Strange World of Quantum Mechanics

A particle of mass M moves in an infinite square well of width L (the “particle in a box”). Classically, the motion has period L2M/E, which depends on the initial condition through the energy E. Quantum mechanically, any wave function repeats exactly with period 4ML2/πℏ, independent of the initial condition. Given this qualitative difference, how can the classical motion possibly be the limit of the quantal time development? The resolution of this paradox involves the difference between the exact revival (recurrence) of the wave function and the approximate periodicity of expectation values such as 〈x(t)〉. (The latter may recur an odd integral number of times before the full wave function recurs.) The period of the expectation values does depend on the initial condition and can possess the expected classical limit. [An Appendix demonstrates that, under suitably quasiclassical conditions, the quantal time evolution of 〈x(t)〉 passes over to the classical result not only in period, but also in its exact func...

Daniel F. Styer

Papers

Nine formulations of quantum mechanics

Common misconceptions regarding quantum mechanics

Insight into entropy

The Strange World of Quantum Mechanics

Quantum revivals versus classical periodicity in the infinite square well