## Mite

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### Roderich Tumulka - One of the best experts on this subject based on the ideXlab platform.

• ##### Macroscopic and microscopic thermal equilibrium
Annalen der Physik, 2017
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [18].

• ##### macroscopic and microscopic thermal equilibrium
arXiv: Quantum Physics, 2016
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell, then for generic macroscopic systems, including those with MBL, most $\psi$ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [Goldstein et al., Phys.Rev.Lett. 115: 100402 (2015)].

• ##### thermal equilibrium of a macroscopic quantum system in a pure state
Physical Review Letters, 2015
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (Mite). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between Mite and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and Mite. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but Mite fails to hold for any phase point.

### Sheldon Goldstein - One of the best experts on this subject based on the ideXlab platform.

• ##### Macroscopic and microscopic thermal equilibrium
Annalen der Physik, 2017
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [18].

• ##### macroscopic and microscopic thermal equilibrium
arXiv: Quantum Physics, 2016
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell, then for generic macroscopic systems, including those with MBL, most $\psi$ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [Goldstein et al., Phys.Rev.Lett. 115: 100402 (2015)].

• ##### thermal equilibrium of a macroscopic quantum system in a pure state
Physical Review Letters, 2015
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (Mite). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between Mite and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and Mite. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but Mite fails to hold for any phase point.

### Keiko Oku - One of the best experts on this subject based on the ideXlab platform.

• ##### female mating strategy during precopulatory mate guarding in spider Mites
Animal Behaviour, 2009
Co-Authors: Keiko Oku
Abstract:

In some taxa, females choose their mates indirectly by using male combat. In the Kanzawa spider Mite, Tetranychus kanzawai, adult males guard prereproductive quiescent females. In a dual choice experiment, more males first approached females already guarded by a conspecific male than approached solitary females. In further experiments, I examined which factors attracted males during precopulatory mate guarding. Males were not attracted to males not in a mate-guarding position. In contrast, the presence of a nonbreeding individual, a juvenile male or a female in a mate-guarding position did attract conspecific males. These results suggest that the presence of any conspecific individual in a mate-guarding position stimulates quiescent females to produce chemicals that attract males. Guarded quiescent females also attracted the attention of the predatory Mite, Neoseiulus womersleyi, but solitary females did not. Since N. womersleyi search for prey using chemical cues, guarded females that release more chemicals than solitary females are probably in more danger. However, males were not attracted to guarded quiescent females that had been previously exposed to N. womersleyi. Thus, quiescent females appeared to control the release of their chemicals, that is, guarded quiescent females release a male-attractant signal. When more than one male attempts to guard one female, male combat often occurs. I discuss the possibility of indirect mate choice by T. kanzawai females during precopulatory mate guarding facilitated by the use of male-attractant signals.

### Joel L. Lebowitz - One of the best experts on this subject based on the ideXlab platform.

• ##### Macroscopic and microscopic thermal equilibrium
Annalen der Physik, 2017
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [18].

• ##### macroscopic and microscopic thermal equilibrium
arXiv: Quantum Physics, 2016
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell, then for generic macroscopic systems, including those with MBL, most $\psi$ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [Goldstein et al., Phys.Rev.Lett. 115: 100402 (2015)].

• ##### thermal equilibrium of a macroscopic quantum system in a pure state
Physical Review Letters, 2015
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (Mite). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between Mite and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and Mite. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but Mite fails to hold for any phase point.

### David A. Huse - One of the best experts on this subject based on the ideXlab platform.

• ##### Macroscopic and microscopic thermal equilibrium
Annalen der Physik, 2017
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [18].

• ##### macroscopic and microscopic thermal equilibrium
arXiv: Quantum Physics, 2016
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (Mite). The distinction between Mite and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell, then for generic macroscopic systems, including those with MBL, most $\psi$ are in both MATE and Mite. We explore here the properties of MATE and Mite and compare the two notions, thereby elaborating on ideas introduced in [Goldstein et al., Phys.Rev.Lett. 115: 100402 (2015)].

• ##### thermal equilibrium of a macroscopic quantum system in a pure state
Physical Review Letters, 2015
Co-Authors: Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Roderich Tumulka
Abstract:

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (Mite). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between Mite and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in Mite while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and Mite. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but Mite fails to hold for any phase point.