Game theory, the formalized study of strategy, began in the 1940s by asking how emotionless geniuses should play games, but ignored until recently how average people with emotions and limited foresight actually play games. This book marks the first substantial and authoritative effort to close this gap. Colin Camerer, one of the field's leading figures, uses psychological principles and hundreds of experiments to develop mathematical theories of reciprocity, limited strategizing, and learning, which help predict what real people and companies do in strategic situations. Unifying a wealth of information from ongoing studies in strategic behavior, he takes the experimental science of behavioral economics a major step forward. He does so in lucid, friendly prose.

	Behavioral game theory has three ingredients that come clearly into focus in this book: mathematical theories of how moral obligation and vengeance affect the way people bargain and trust each other; a theory of how limits in the brain constrain the number of steps of "I think he thinks . . ." reasoning people naturally do; and a theory of how people learn from experience to make better strategic decisions. Strategic interactions that can be explained by behavioral game theory include bargaining, games of bluffing as in sports and poker, strikes, how conventions help coordinate a joint activity, price competition and patent races, and building up reputations for trustworthiness or ruthlessness in business or life.

	While there are many books on standard game theory that address the way ideally rational actors operate, Behavioral Game Theory stands alone in blending experimental evidence and psychology in a mathematical theory of normal strategic behavior. It is must reading for anyone who seeks a more complete understanding of strategic thinking, from professional economists to scholars and students of economics, management studies, psychology, political science, anthropology, and biology.

Behavioral Game Theory: Experiments in Strategic Interaction

The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.

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The density-matrix renormalization group in the age of matrix product states

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

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

Quantum thermodynamics

Entanglement within a given device provides a potential resource for quantum information processing. Entanglement between system and environment leads to decoherence (thus suppressing non-classical features within the system) but also opens up a route to robust and universal control. The latter is related to thermodynamic equilibrium, a generic behavior of bi-partite quantum systems. Fingerprints of this equilibrium behavior (including relaxation and stability) show up already far from the thermodynamic limit, where a complete solution of the underlying Schrodinger dynamics of the total system is still feasible.

Emergence of thermodynamic behavior within composite quantum systems

Background- Basics of Quantum Mechanics- Basics of Thermodynamics and Statistics- Brief Review of Pertinent Concepts- Equilibrium- The Program for the Foundation of Thermodynamics- Outline of the Present Approach- Dynamics and Averages in Hilbert Space- Typicality of Observables and States- System and Environment- The Typical Reduced State of the System- Entanglement, Correlations and Local Entropy- Generic Spectra of Large Systems- Temperature- Pressure and Adiabatic Processes- Quantum Mechanical and Classical State Densities- Equilibration in Model Systems- Non-Equilibrium- Brief Review of Relaxation and Transport Theories- Projection Operator Techniques and Hilbert Space Average Method- Finite Systems as Thermostats- Projective Approach to Dynamical Transport- Open System Approach to Transport- Applications and Models- Purity and Local Entropy in Product Hilbert Space- Observability of Intensive Variables- Observability of Extensive Variables- Quantum Thermodynamic Processes

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Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems

We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate quantum master equations. The standard microscopic derivation of the weak-coupling Lindblad equation in the secular approximation is considered, and shown to be inadequate for the description of stationary nonequilibrium properties like a nonvanishing energy current. Furthermore, we derive an alternative master equation that is capable of describing a stationary energy current and, at the same time, leads to a completely positive dynamical map. This paves the way for efficient numerical investigations of heat transport in larger systems based on Monte Carlo wave function techniques.

https://arxiv.org/pdf/quant-ph/0703048.pdf

Modeling heat transport through completely positive maps

Based on quantum thermodynamic reasoning even small embedded systems S may well be in thermodynamic equilibrium. This equilibrium depends on the system, here formalized by a parameter γ controlling the spectrum of S and on the embedding, formalized via a parameter α controlling the resulting attractor state for S. Cyclic processes in this α/γ-control space will be investigated and the effects of non-equilibrium studied.

Jochen Gemmer

Papers

Quantum thermodynamics

Emergence of thermodynamic behavior within composite quantum systems

Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems

Modeling heat transport through completely positive maps

Quantum Thermodynamic Processes