FINDING: Decoherence is the mechanism by which quantum superpositions irreversibly leak into the environment, effectively collapsing the wavefunction and generating the classical arrow of time; recent work focuses on exact master equations for non-Markovian decoherence in quantum dot systems. | MATH: The core mathematical object is the reduced density matrix $\rho_S(t) = \mathrm{Tr}_E[U(t)\rho_{SE}(0)U^\dagger(t)]$ , with the Feynman–Vernon influence functional $F[J] = \exp\left(-\frac{1}{\hbar}\int_0^t\int_0^t J(t') \tilde{D}(t'-t'') J(t'') dt' dt''\right)$ . The exact master equation (from the arXiv paper) takes the form $\dot{\rho}_S = -\frac{i}{\hbar}[H_S,\rho_S] - \frac{i}{\hbar}\Delta(t)[x^2,\rho_S] - \gamma(t)[x,\{p,\rho_S\}] - D(t)[x,[x,\rho_S]] - \bar{D}(t)[x,\{p,\rho_S\}]$ , where $\gamma(t)$ is the time-dependent damping, $D(t)$ the normal diffusion, and $\bar{D}(t)$ the anomalous diffusion coefficient. Decoherence time scales as $\tau_d \sim \hbar^2 / (m k_B T \De Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Decoherence is the mechanism by which quantum superpositions irreversibly leak into the environment, effectively collapsing the wavefunction and generating the classical arrow of time; recent work focuses on exact master equations for non-Markovian decoherence in quantum dot systems. | MATH: The core mathematical object is the reduced density matrix \(\rho_S(t) = \mathrm{Tr}_E[U(t)\rho_{SE}(0)U^\dagger(t)]$, with the Feynman–Vernon influence functional $F[J] = \exp\left(-\frac{1}{\hbar}\int_0^t\int_0^t J(t') \tilde{D}(t'-t'') J(t'') dt' dt''\right)$. The exact master equation (from the arXiv paper) takes the form $\dot{\rho}_S = -\frac{i}{\hbar}[H_S,\rho_S] - \frac{i}{\hbar}\Delta(t)[x^2,\rho_S] - \gamma(t)[x,\{p,\rho_S\}] - D(t)[x,[x,\rho_S]] - \bar{D}(t)[x,\{p,\rho_S\}]$, where $\gamma(t)$ is the time-dependent damping, $D(t)$ the normal diffusion, and $\bar{D}(t)$ the anomalous diffusion coefficient. Decoherence time scales as \(\tau_d \sim \hbar^2 / (m k_B T \De Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 9, 20260 citations

The Arrow of Time and Its Irreversibility

Gerald F. Thomas

Jan 1, 20230 citations

Quantum Dynamics With Intrinsic Time Asymmetry and Indistinguishable Events

Peter William Bryant

The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a master equation or a phase-destroying, non-Hermitian Hamiltonian operator. As an application, we calculate predictive probabilities for the decoherence measured in Rabi oscillations experiments. We can also show that a previously puzzling experimental result, unexplained within the formalism of the quantum master equation, is in fact expected and is the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a master equation or a phase-destroying, non-Hermitian Hamiltonian operator. As an application, we calculate predictive probabilities for the decoherence measured in Rabi oscillations experiments. We can also show that a previously puzzling experimental result, unexplained within the formalism of the quantum master equation, is in fact expected and is the measurable consequence of the indistinguishability of separate, uncontrolled interactions between systems and their environment.

arXiv:0906.5205Jun 29, 20090 citations

Time's arrow and external perturbations

P. Morrison

Jan 1, 19668 citations

Scales and Granularity: Resolving the Arrow of Time Paradox Between Mechanics and Thermodynamics

changzheng zhou, ZIQING zhou

The arrow of time paradox between quantum mechanics and thermodynamicsarises from the fundamental conflict between the time-symmetric evolution of thewave function and the irreversible increase of thermodynamic entropy. This pa?per introduces a ”small observer” model with quantum resolution capabilities andcombines quantum measurement theory with open quantum system dynamics toreveal the influence of observer scales on the perception of the arrow of time. Byestablishing a quantum master equation model for N coupled small observers, wedemonstrate the emergence of macroscopic thermodynamic entropy from micro?scopic quantum entropy production, providing a novel theoretical framework forunifying the understanding of the arrow of time. Numerical simulations based onthe quantum Darwinism framework validate the theoretical predictions.The arrow of time paradox between quantum mechanics and thermodynamicsarises from the fundamental conflict between the time-symmetric evolution of thewave function and the irreversible increase of thermodynamic entropy. This pa?per introduces a ”small observer” model with quantum resolution capabilities andcombines quantum measurement theory with open quantum system dynamics toreveal the influence of observer scales on the perception of the arrow of time. Byestablishing a quantum master equation model for N coupled small observers, wedemonstrate the emergence of macroscopic thermodynamic entropy from micro?scopic quantum entropy production, providing a novel theoretical framework forunifying the understanding of the arrow of time. Numerical simulations based onthe quantum Darwinism framework validate the theoretical predictions.

Feb 19, 20250 citations

A convenient expansion of the master equation

G. L. Braglia

Physics Letters AJul 1, 19761 citation

\rho_S(t) = \mathrm{Tr}_E[U(t)\rho_{SE}(0)U^\dagger(t)]

, with the Feynman–Vernon influence functional

F[J] = \exp\left(-\frac{1}{\hbar}\int_0^t\int_0^t J(t') \tilde{D}(t'-t'') J(t'') dt' dt''\right)

. The exact master equation (from the arXiv paper) takes the form

\dot{\rho}_S = -\frac{i}{\hbar}[H_S,\rho_S] - \frac{i}{\hbar}\Delta(t)[x^2,\rho_S] - \gamma(t)[x,\{p,\rho_S\}] - D(t)[x,[x,\rho_S]] - \bar{D}(t)[x,\{p,\rho_S\}]

, where

\gamma(t)

is the time-dependent damping,

D(t)

the normal diffusion, and

\bar{D}(t)

the anomalous diffusion coefficient. Decoherence time scales as \(\tau_d \sim \hbar^2 / (m k_B T \De Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com