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Intensive studies on light–matter interactions and technological breakthroughs, especially conducted in the field of dressed photon research, have led to a growing concern regarding unsettled off-shell quantum field interactions. The Special Issue, entitled “Quantum Fields and Off-Shell Sciences”, was organized to promote the progress of such research activities from a wider perspective, not limited to dressed photon studies. This book contains excellent papers that were published in this Special Issue. It will provide scientific and technical information on the quantum fields and off-shell sciences to scientists, engineers, and students who are and will be engaged in this field.

Research & information: general --- Physics --- dressed photon --- dressed photon constant --- natural units --- Heisenberg cut --- de Sitter space --- dark energy --- dark matter --- cosmological constant --- twin universes --- conformal cyclic cosmology --- quantum walk --- scattering theory --- energy --- survival probability --- attractor eigenspace --- category --- algebra --- state --- category algebra --- state on category --- noncommutative probability --- quantum probability --- GNS representation --- quantum measurement --- C*-algebra --- algebraic quantum field theory --- local net --- extension of local net --- completely positive instrument --- macroscopic distinguishability --- Grassmann manifold --- flag manifold --- pre-homogeneous vector space --- invariants --- category theory --- nonstandard analysis --- coarse geometry --- quantum field --- combinatorial optimization --- Ising spin glass --- coupled oscillator --- eigenmode --- clustering --- localization --- dissipation --- off-shell science --- non-equilibrium open system --- quantum master equation --- quantum density matrix --- projection operator --- renormalization --- discrete-time quantum walk --- scattering quantum random walk --- Grover walk --- pathfinding --- network

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The field of chaos in many-body quantum systems has a long history, going back to Wigner’s simple models for heavy nuclei. Quantum chaos is being investigated in a broad variety of experimental platforms such as heavy nuclei, driven (few-electron) atoms, ultracold quantum gases, and photonic or microwave realizations. Quantum chaos plays a new and important role in many branches of physics, from condensed matter problems of many-body localization, including thermalization studies in closed and open quantum systems, and the question of dynamical stability relevant for quantum information and quantum simulation. This Special Issue and its related book address theories and experiments, methods from classical chaos, semiclassics, and random matrix theory, as well as many-body condensed matter physics. It is dedicated to Prof. Shmuel Fishman, who was one of the major representatives of the field over almost four decades, who passed away in 2019.

quantum chaos --- decoherence --- Arnol’d cat --- classical limit --- correspondence principle --- cold atoms --- interacting fermions --- thermalization --- dynamical chaos --- Sinai oscillator --- quantum tunneling --- dissipation --- effective action --- quantum transport --- nonlinear Schrödinger equation --- Gross-Pitaevskii equation --- Schrödinger-Poisson equation --- Bose-Einstein condensate --- dark matter --- periodically kicked system --- Lorentzian potential --- topological horseshoe --- uniformly hyperbolicity --- sector condition --- fractal Weyl law --- survival probability --- correlation functions --- semiclassical approximation --- revival dynamics --- Morse oscillator --- atom-optics kicked rotor --- quantum resonance --- continuous-time quantum walks --- Bose–Einstein condensates --- quantum interference --- Aubry-André model --- correlation hole --- fluctuation theorems --- nonequilibrium statistical mechanics --- quantum thermodynamics --- phase transitions --- Dirac bosons --- mean field analysis --- adiabatic separation --- trapped ions --- Frenkel–Kontorova --- long–range interactions --- sine-Gordon kink --- quantum kicked rotor --- Anderson localisation --- dynamical localisation

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The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited to: Markov chains and processes; large deviations and limit theorems; random motions; stochastic biological model; reliability, availability, maintenance, inspection; queueing models; queueing network models; computational methods for stochastic models; applications to risk theory, insurance and mathematical finance.

recursive formula --- rate of convergence --- asymptotic approximation --- parabolic equation --- processor heating and cooling --- compound poisson insurance risk model --- Koksma-Hlawka inequality --- phase-type service time distribution --- discrete-time Geo/D/1 queue --- lower record values --- Fourier-cosine series --- retrials --- state-dependent marked Markovian arrival process --- queuing network --- stochastic processes --- Laplace transform --- von-Neumann–Ulam scheme --- Monte Carlo method --- Lévy process --- Wiener–Poisson risk model --- queueing systems --- quasi-random sequences --- closed-form solution --- Cauchy problem --- product form --- estimation --- extreme order statistics --- guaranteed minimum death benefit --- valuation --- multidimensional birth-death process --- Markovian queueing models --- survival probability --- truncated distribution --- Markovian arrival process --- inhomogeneous continuous-time Markov chain --- measure of information --- option --- unbiased estimator --- matrix-geometric solution --- Dickson–Hipp operator --- Fourier transform --- multi-class arrival processes --- total precipitation volume --- one dimensional projection --- random sample size --- markovian arrival process --- cumulative inaccuracy --- mutual information --- Quasi-Birth-and-Death process --- limiting characteristics --- testing statistical hypotheses --- wet periods --- compound Poisson risk model --- time-dependent queue-length probability --- non-stationary --- equity-linked death benefits --- wireless telecommunication networks --- Fourier cosine series expansion --- impatience --- generalized Gerber–Shiu discounted penalty function --- quasi-Monte Carlo method --- expected discounted penalty function --- Nonparametric threshold estimation

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Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era.

Research & information: general --- Mathematics & science --- energy --- economic growth --- output elasticities --- entropy production --- emissions --- optimization --- speculative attacks --- currency crisis --- neural networks --- deep learning --- Quantum-Inspired Neural Network --- traveling salesman problem --- simulated annealing technique --- kinetic exchange model --- Gini index --- Kolkata index --- minority game --- Kolkata Paise Restaurant problem --- time series analysis --- cross-correlations --- power law classification scheme --- network analysis --- globalisation --- entropy --- portfolio optimization --- regularization --- renormalization --- econophysics --- highway freight transportation --- radiation model --- transportation network --- network diversity --- power law --- economic development --- decision-making --- bounded rationality --- complexity economics --- information-theory --- maximum entropy principle --- quantal response statistical equilibrium --- correlation coefficient --- detrended cross-correlation analysis --- COVID-19 --- mobility indices --- random geometry --- risk measurement --- disordered systems --- replica theory --- return distributions --- power-law tails --- stretched exponentials --- q-Gaussians --- financial markets --- financial complexity --- collective intelligence --- emergent property --- stock correlation --- lexical evolution of econophysics --- text as data --- correspondence analysis --- long-range memory --- 1/f noise --- absolute value estimator --- anomalous diffusion --- ARFIMA --- first-passage times --- fractional Lèvy stable motion --- Higuchi's method --- mean squared displacement --- multiplicative point process --- correlation filtering --- minimal spanning tree --- planar maximally filtered graph --- topological data analysis --- SGX --- TAIEX --- complex systems --- ecological economics --- urban-regional economics --- income distribution --- financial market dynamics --- income tax --- tax deduction --- income redistribution --- government transfer --- government dependency --- poverty line --- basic income guarantee --- effective tax rate --- balanced budget --- elastic tax --- Cantor set --- fractals --- homeomorphism --- detrended fluctuation analysis --- Hurst exponent --- continuous time random walk --- intertrade times --- volatility clustering --- local transfer entropy --- long-short-term-memory --- Bitcoin --- cryptocurrencies --- multiscale analysis --- detrended cross-correlations --- covariance matrices --- copulas --- high-frequency trading --- market stability --- agent-based models --- structural entropy --- Economic Freedom of the World index --- Index of Economic Freedom --- rank-size law technique --- power law behaviour --- exponential behaviour --- multiscale partition function --- multifractal analysis --- company market --- export readiness --- internationalization --- options pricing --- mortality --- companies --- start-up --- FTSE100 --- Gompertz --- MinMax --- survival probability distribution --- high-frequency trader --- multivariate Hawkes process --- forex market --- wealth distribution --- kinetic models --- wealth inequalities --- compartmental epidemic modelling --- vaccination campaign --- flash crash --- systemic risk --- financial networks --- high frequency trading --- market microstructure --- phase transition --- criticality --- dynamics of complex networks --- cascading failure --- network science --- economic complexity --- relatedness --- products and services --- planar graph --- partial correlation --- discounting --- bond pricing --- real interest rates --- calendar anomalies --- day-of-the-week effect --- market indices --- multifractal detrended fluctuation analysis