Equilibration properties of small quantum systems: further examples

Luck, J. M.

doi:10.1088/1751-8121/aa7f94

Cited by 3 publications

(1 citation statement)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the non perturbative side, the Bethe Ansatz [15] provides some exact diagonalization results but only for specific classes of Hamiltonians, see e.g. [16][17][18]. If one focuses on the particular problem of finding only the spectrum of Ĥ0 + Ŵ for arbitrary given matrices Ĥ0 and Ŵ , this is a very difficult problem [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Ithier¹,

Ascroft²

2018

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We present a non perturbative calculation technique providing the mixed moments of the overlaps between the eigenvectors of two large quantum Hamiltonians:Ĥ0 andĤ0 +Ŵ , whereĤ0 is deterministic andŴ is random. We apply this method to recover the second order moments or Local Density Of States in the case of an arbitrary fixedĤ0 and a GaussianŴ . Then we calculate the fourth order moments of the overlaps in the same setting. Such quantities are crucial for understanding the local dynamics of a large composite quantum system. In this case,Ĥ0 is the sum of the Hamiltonians of the system subparts andŴ is an interaction term. We test our predictions with numerical simulations. arXiv:1803.08122v1 [quant-ph]

show abstract

Section: Introductionmentioning

confidence: 99%

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Ithier¹,

Ascroft²

2018

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Hilbert space average of transition probabilities

2020

View full text Add to dashboard Cite

Typical equilibrium state of an embedded quantum system

2017

View full text Add to dashboard Cite

We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded quantum system was established for several classes of random interactions. In other words, the time evolution of its quantum state does not depend on the microscopic details of the interaction. Focusing at the long time regime, we use this property to calculate analytically a new partition function characterizing the stationary state and involving the overlaps between eigenvectors of a bare and a dressed Hamiltonian. This partition function provides a new thermodynamical ensemble which includes the microcanonical and canonical ensembles as particular cases. We check our predictions with numerical simulations.In what state of equilibrium can a quantum system be? Does this state have universal properties and what are the conditions for its emergence? These questions are not new, dating even from the very birth of quantum theory [1] and are surprisingly open [2,3]. Indeed, the foundations of statistical physics still rely today on a static Bayesian point of view assuming the equiprobability of the accessible states defining the microcanonical ensemble. Assuming temperature and chemical potential can be defined then the canonical and grand canonical ensembles can be derived, allowing to calculate all relevant macroscopic quantities in the thermodynamical limit [4][5][6]. In order to link theoretical predictions calculated with averages over these ensembles to experimental quantities measured on a single system, an assumption of ergodicity is made. Despite being broadly accepted, this assumption is not justified in a satisfactory manner (see, e.g., the discussion in Ref. [7]). Triggered by recent progress in the quantum engineering of mesoscopic systems [8,9], some theoretical progress has been achieved for attempting to explain thermodynamical equilibrium with a purely quantum point of view.From the early work of von Neumann on quantum ergodicity [1,10], most theoretical studies aiming at understanding thermalisation as a quantum and universal [11] process have focused on looking for signatures of thermalisation on physical observables of large quantum systems [12][13][14][15], for instance with the Eigenstate Thermalisation Hypothesis (ETH) surmise [16][17][18]. Instead of observables, one can also focus on the state of a system embedded in a larger one for which a "canonical typicality" property has been established: the overwhelming majority of pure quantum states of the composite system are locally [19] canonical [20][21][22]. This static "typicality" has been extended to the dynamics of embedded quantum systems (two-level [23], four-level [24] and arbitrary [25] quantum systems). We apply here this "dynamical typicality" property in order to calculate analytically and with full generality the stationary state of an embedded quantum system at long time. We find a new thermody...

show abstract

Equilibration properties of small quantum systems: further examples

Cited by 3 publications

References 63 publications

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Hilbert space average of transition probabilities

Typical equilibrium state of an embedded quantum system

Contact Info

Product

Resources

About