Abstract We discuss what kind of quantum dynamics can yield thermalization. We show that any temperature measurement protocol must be sensitive to the system’s local energy scale, not just its state. Specifically, we illustrate this by showing that any temperature measurement protocol that does not resolve the system’s local Hamiltonian (such as, e.g. full state tomography) is susceptible to being fooled into measuring any value for the temperature. Since placing a system in thermal contact with a reference system at a known temperature is a way of measuring temperature, any robust notion of thermal contact must be resistant to this ‘attack’. This provides us with a necessary conditions for thermal contact between quantum systems. We then apply this condition to a scenario where one expects to find thermalization: a system repeatedly interacting with the microconstitutents of a thermal reservoir. We show such models of thermalization cannot be correct without fine-tuning.Abstract We discuss what kind of quantum dynamics can yield thermalization. We show that any temperature measurement protocol must be sensitive to the system’s local energy scale, not just its state. Specifically, we illustrate this by showing that any temperature measurement protocol that does not resolve the system’s local Hamiltonian (such as, e.g. full state tomography) is susceptible to being fooled into measuring any value for the temperature. Since placing a system in thermal contact with a reference system at a known temperature is a way of measuring temperature, any robust notion of thermal contact must be resistant to this ‘attack’. This provides us with a necessary conditions for thermal contact between quantum systems. We then apply this condition to a scenario where one expects to find thermalization: a system repeatedly interacting with the microconstitutents of a thermal reservoir. We show such models of thermalization cannot be correct without fine-tuning.

arXiv:1805.11118Journal of Physics A Mathematical and TheoreticalAug 9, 20192 citations

The Eigenstate Thermalization Hypothesis in a Quantum Point Contact Geometry

Gregory Levine, Barry Friedman

It is known that the long-range quantum entanglement exhibited in free fermion systems is sufficient to "thermalize" a small subsystem in that the subsystem reduced density matrix computed from a typical excited eigenstate of the combined system is approximately thermal. Remarkably, fermions without any interactions are thus thought to satisfy the Eigenstate Thermalization Hypothesis (ETH). We explore this hypothesis when the fermion subsystem is only minimally coupled to a quantum reservoir (in the form of another fermion system) through a quantum point contact (QPC). The entanglement entropy of two 2-d free fermion systems connected by one or more quantum point contacts (QPC) is examined at finite energy and in the ground state. When the combined system is in a typical excited state, it is shown that the entanglement entropy of a subsystem connected by a small number of QPCs is sub-extensive, scaling as the linear size of the subsystem ( $L_A$ ). For sufficiently low energies ( $E$ ) and small subsystems, it is demonstrated numerically that the entanglement entropy $S_A \sim L_A E$ , what one would expect for the thermodynamics of a one-dimensional system. In this limit, we suggest that the entropy carried by each additional QPC is quantized using the one-dimensional finite size/temperature conformal scaling: $ΔS_A = α\log{(1/E)\sinh{(L_AE)}}$ . The sub-extensive entropy in the case of a small number of QPCs should be contrasted with the expectation for both classical, ergodic systems and quantum chaotic systems wherein a restricted geometry might affect the equilibrium relaxation times, but not the equilibrium properties themselves, such as extensive entropy and heat capacity.It is known that the long-range quantum entanglement exhibited in free fermion systems is sufficient to "thermalize" a small subsystem in that the subsystem reduced density matrix computed from a typical excited eigenstate of the combined system is approximately thermal. Remarkably, fermions without any interactions are thus thought to satisfy the Eigenstate Thermalization Hypothesis (ETH). We explore this hypothesis when the fermion subsystem is only minimally coupled to a quantum reservoir (in the form of another fermion system) through a quantum point contact (QPC). The entanglement entropy of two 2-d free fermion systems connected by one or more quantum point contacts (QPC) is examined at finite energy and in the ground state. When the combined system is in a typical excited state, it is shown that the entanglement entropy of a subsystem connected by a small number of QPCs is sub-extensive, scaling as the linear size of the subsystem ($L_A$). For sufficiently low energies ($E$) and small subsystems, it is demonstrated numerically that the entanglement entropy $S_A \sim L_A E$, what one would expect for the thermodynamics of a one-dimensional system. In this limit, we suggest that the entropy carried by each additional QPC is quantized using the one-dimensional finite size/temperature conformal scaling: $ΔS_A = α\log{(1/E)\sinh{(L_AE)}}$. The sub-extensive entropy in the case of a small number of QPCs should be contrasted with the expectation for both classical, ergodic systems and quantum chaotic systems wherein a restricted geometry might affect the equilibrium relaxation times, but not the equilibrium properties themselves, such as extensive entropy and heat capacity.

arXiv:2501.03076Jan 6, 20250 citations

THERMAL PHASES IN FINITE QUANTUM SYSTEMS

David J. Dean

Recent Progress in Many-Body TheoriesDec 1, 20020 citations

Approach to thermal equilibrium of macroscopic quantum systems

Sheldon Goldstein, Joel L. Lebowitz, Christian Mastrodonato +2 more

WORLD SCIENTIFIC eBooksAug 1, 20250 citations

Sudden change of the thermal contact between two quantum systems

Juan Restrepo, S. Camalet

In this paper, we address the issue of the stability of the thermal equilibrium of large quantum systems with respect to variations of the thermal contact between them. We study the Schrödinger time evolution of a free bosonic field in two coupled one-dimensional cavities after a sudden change of the contact between the cavities. Although this coupling is thermodynamically small, modifying it has a considerable impact on the two-point correlation functions of the system. We find that they do not return to equilibrium but essentially oscillate with a period proportional to the length of the cavities. We compare this coupled cavities system with the perfect gas, which is described by similar expressions but behaves very differently.In this paper, we address the issue of the stability of the thermal equilibrium of large quantum systems with respect to variations of the thermal contact between them. We study the Schrödinger time evolution of a free bosonic field in two coupled one-dimensional cavities after a sudden change of the contact between the cavities. Although this coupling is thermodynamically small, modifying it has a considerable impact on the two-point correlation functions of the system. We find that they do not return to equilibrium but essentially oscillate with a period proportional to the length of the cavities. We compare this coupled cavities system with the perfect gas, which is described by similar expressions but behaves very differently.

arXiv:0905.1079New Journal of PhysicsMay 28, 20101 citation

L_A

). For sufficiently low energies (

E

) and small subsystems, it is demonstrated numerically that the entanglement entropy

S_A \sim L_A E

, what one would expect for the thermodynamics of a one-dimensional system. In this limit, we suggest that the entropy carried by each additional QPC is quantized using the one-dimensional finite size/temperature conformal scaling:

ΔS_A = α\log{(1/E)\sinh{(L_AE)}}

. The sub-extensive entropy in the case of a small number of QPCs should be contrasted with the expectation for both classical, ergodic systems and quantum chaotic systems wherein a restricted geometry might affect the equilibrium relaxation times, but not the equilibrium properties themselves, such as extensive entropy and heat capacity.