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Long-time diffusion for a quantum particle

Wojciech De Roeck

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter reviews and summarizes some recent progress on the rigorous derivation of irreversible behaviour in simple models of open quantum systems, in particular spins and particles interacting ... More


Finite Quantum Systems

Robert Alicki and Mark Fannes

in Quantum Dynamical Systems

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Quantum systems with a discrete dynamical spectrum, such as finite dimensional systems or particles confined to a finite volume, cannot exhibit true ergodic behaviour. Nevertheless, scaling limits ... More


Economic Theory and Ecological Limits

Ramprasad Sengupta

in Ecological Limits and Economic Development

Published in print:
2013
Published Online:
May 2013
ISBN:
9780198081654
eISBN:
9780199082407
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198081654.003.0002
Subject:
Economics and Finance, Development, Growth, and Environmental

The chapter shows how the ecological limits to economic scale affecting the human well-being have been accommodated and analysed in the micro and the macroeconomic theory by treating the consequent ... More


Renormalization group approach to matrix models

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0025
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 25 discusses how, in the mid–1980s, it was realized that some ensembles of random matrices in the large size and double scaling limit could be used as toy models for two–dimensional quantum ... More


Random tensor models—the U(N)D-invariant model

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the ... More


Random tensor models—the multi-orientable (MO) model

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In its first section, this chapter presents the definition of the multi-orientable tensor model. The 1/N expansion and the large N limit of this model are exposed in the second section of the ... More


From random matrices to random tensors

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

After a brief presentation of random matrices as a random surface QFT approach to 2D quantum gravity, we focus on two crucial mathematical physics results: the implementation of the large N limit (N ... More


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