# Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

@article{Balz2018DynamicalTF, title={Dynamical typicality for initial states with a preset measurement statistics of several commuting observables}, author={Ben N Balz and Johannes Richter and Jochen Gemmer and Robin Steinigeweg and Peter Reimann}, journal={arXiv: Statistical Mechanics}, year={2018} }

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schrodinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This…

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## References

SHOWING 1-10 OF 76 REFERENCES

### Dynamical typicality of quantum expectation values.

- MathematicsPhysical review letters
- 2009

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at…

### Equilibration of isolated many-body quantum systems with respect to general distinguishability measures.

- PhysicsPhysical review. E
- 2016

We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady…

### Dynamical Typicality Approach to Eigenstate Thermalization.

- PhysicsPhysical review letters
- 2018

It is shown by means of a dynamical typicality approach that most initial states within a microcanonical energy shell of an isolated many-body quantum system exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH).

### Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed provided all these…

### Typicality for Generalized Microcanonical Ensembles

- Physics
- 2007

For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability…

### Equilibration of isolated macroscopic quantum systems

- Physics
- 2012

We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any…

### Spin-current autocorrelations from single pure-state propagation.

- PhysicsPhysical review letters
- 2014

It is demonstrated that the concept of quantum typicality allows for significant progress in the study of real-time spin dynamics and transport in quantum magnets and provides a new benchmark for the enigmatic spin Drude weight.

### Canonical thermal pure quantum state.

- PhysicsPhysical review letters
- 2013

The TPQ formulation of statistical mechanics is established, according to which all quantities of statistical-mechanical interest are obtained from a single realization of any TPQ state, and it is shown that it has great advantages in practical applications.

### Canonical typicality.

- PhysicsPhysical review letters
- 2006

This work clarifies, expands, and justifies remarks made by Schrödinger in 1952, that a much stronger statement holds for quantum systems when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell.

### Regression relation for pure quantum states and its implications for efficient computing.

- PhysicsPhysical review letters
- 2013

A modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many- body quantum systems is obtained and it is shown that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians.