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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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