Sign of the Feynman Propagator and Irreversibility

• URL: http://arxiv.org/abs/2204.06928v2
• Date: Tue, 17 Jan 2023 17:52:43 GMT
• Title: Sign of the Feynman Propagator and Irreversibility
• Authors: Allan Tameshtit
• Abstract summary: We show that the sign property, $ operatornameRe iDelta_F,int geq 0 $, hinges on the reversibility of time evolution. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $ operatornameRe iDelta_F,int $ is generally lost.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: For the interacting Feynman propagator $ \Delta_{F,int}(x,y) $ of scalar electrodynamics, we show that the sign property, $ \operatorname{Re} i\Delta_{F,int} \geq 0 $, hinges on the reversibility of time evolution. In contrast, $ \operatorname{Im} i\Delta_{F,int} $ is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $ \operatorname{Re} i\Delta_{F,int} $ is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

Related papers

• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization [0.0]
  We derive general bounds for the operator norm of this commutator in free and interacting fermionic systems. We show, in particular, that in a localized system the norm does grow at most exponentially.
  arXiv  Detail & Related papers  (2024-01-16T00:57:09Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• On Schr\"{o}dinger Operators Modified by $\delta$ Interactions [0.0]
  We show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of $H_0$. We derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant. We consider the possible extensions of our results to the multi center case, to $delta$ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold.
  arXiv  Detail & Related papers  (2023-04-03T19:48:42Z)
• Statistical Learning under Heterogeneous Distribution Shift [71.8393170225794]
  Ground-truth predictor is additive $mathbbE[mathbfz mid mathbfx,mathbfy] = f_star(mathbfx) +g_star(mathbfy)$.
  arXiv  Detail & Related papers  (2023-02-27T16:34:21Z)
• The Sample Complexity of Online Contract Design [120.9833763323407]
  We study the hidden-action principal-agent problem in an online setting. In each round, the principal posts a contract that specifies the payment to the agent based on each outcome. The agent then makes a strategic choice of action that maximizes her own utility, but the action is not directly observable by the principal.
  arXiv  Detail & Related papers  (2022-11-10T17:59:42Z)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• On Yang-Mills Stability Bounds and Plaquette Field Generating Function [0.0]
  We consider the Yang-Mills (YM) QFT with group $U(N)$. For free and periodic b.c., we show thermodynamic and stability bounds for a normalized partition function of any YM model. Our methods are an alternative and complete the more traditional ones.
  arXiv  Detail & Related papers  (2022-05-15T20:48:10Z)
• Periodically driven Rydberg chains with staggered detuning [0.0]
  We study the stroboscopic dynamics of a driven finite Rydberg chain with staggered ($Delta$) and time-dependent uniform ($lambda(t)$) detuning terms using exact diagonalization (ED) We show that at intermediate drive ($omega_D$), the presence of a finite $Delta$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density density correlation function at specific $omega_D
  arXiv  Detail & Related papers  (2021-12-29T19:04:07Z)
• Simulated annealing from continuum to discretization: a convergence analysis via the Eyring--Kramers law [10.406659081400354]
  We study the convergence rate of continuous-time simulated annealing $(X_t;, t ge 0)$ and its discretization $(x_k;, k =0,1, ldots)$ We prove that the tail probability $mathbbP(f(X_t) > min f +delta)$ (resp. $mathP(f(x_k) > min f +delta)$) decays in time (resp. in cumulative step size)
  arXiv  Detail & Related papers  (2021-02-03T23:45:39Z)
• Perelman's Ricci Flow in Topological Quantum Gravity [62.997667081978825]
  In our quantum gravity, Perelman's $tau$ turns out to play the role of a dilaton for anisotropic scale transformations. We show how Perelman's $cal F$ and $cal W$ entropy functionals are related to our superpotential.
  arXiv  Detail & Related papers  (2020-11-24T06:29:35Z)
• GO Hessian for Expectation-Based Objectives [73.06986780804269]
  GO gradient was proposed recently for expectation-based objectives $mathbbE_q_boldsymbolboldsymbolgamma(boldsymboly) [f(boldsymboly)]$. Based on the GO gradient, we present for $mathbbE_q_boldsymbolboldsymbolgamma(boldsymboly) [f(boldsymboly)]$ an unbiased low-variance Hessian estimator, named GO Hessian.
  arXiv  Detail & Related papers  (2020-06-16T02:20:41Z)
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots [4.203229514770571]
  Operator square-roots are ubiquitous in theoretical physics. We show that under certain conditions differential equations can be derived which can be used to find perturbatively inaccessible approximations to operator square-roots. We apply our approach to the zero mass Klein-Gordon Hamiltonian in a constant magnetic field, and as a main application, the Holstein-Primakoff representation of spin operators.
  arXiv  Detail & Related papers  (2020-06-11T23:22:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.