Related papers: Eigenstate Thermalisation on Average
The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions…
To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. Despite the fact that the theory is more than 100 years old, we are still discussing its foundations…
An isolated quantum system is said to thermalize if ${\rm Tr} (A \rho(t)) \to {\rm Tr} (A \rho_{\rm eq})$ for time $t \to \infty$. Here $\rho(t)$ is the time-dependent density matrix of the system, $\rho_{\rm eq}$ is the time-independent…
We propose a general method to embed target states into the middle of the energy spectrum of a many-body Hamiltonian as its energy eigenstates. Employing this method, we construct a translationally-invariant local Hamiltonian with no local…
We present a study of thermalisation of a small isolated Hubbard lattice cluster prepared in a pure state with a well-defined energy. We examine how a two-site subsystem of the lattice thermalises with the rest of the system as its…
When studying thermalization of quantum systems, it is typical to ask whether a system interacting with an environment will evolve towards a local thermal state. Here, we show that a more general and relevant question is "when does a system…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we…
Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments…
In the present note, we discuss a simple example of a macroscopic quantum many-body system in which the approach to thermal equilibrium from an arbitrary initial state in the microcanonical energy shell is proved without relying on any…
If and how an isolated quantum system thermalizes despite its unitary time evolution is a long-standing, open problem of many-body physics. The eigenstate thermalization hypothesis (ETH) postulates that thermalization happens at the level…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
Recent work on the subject of isolated quantum thermalization has suggested that an individual energy eigenstate of a non-integrable quantum system may encode a significant amount of information about that system's Hamiltonian. We provide a…
Integrable systems do not obey the strong eigenstate thermalization hypothesis (ETH), which has been proposed as a mechanism of thermalization in isolated quantum systems. It has been suggested that an integrable system reaches a steady…
Quantum thermalization is well understood via the Eigenstate Thermalization Hypothesis (ETH). The general form of ETH, describing all the relevant correlations of matrix elements, may be derived on the basis of a `typicality' argument of…
The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal…
We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our…
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 under generic equilibrium and…
Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. At the core of this theory is…
We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A…