Stochastic unraveling of relativistic quantum measurements

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

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Quantum mechanics

10.1093/oso/9780198802877.003.0002 ◽

2018 ◽

Author(s):

Michael Kachelriess

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Mechanics ◽

Relativistic Quantum ◽

Transition Amplitude ◽

External Source ◽

Quantum Field ◽

Damping Term ◽

Relativistic Quantum Theory ◽

Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

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Why Quantum Measurements Yield Single Values

Foundations of Physics ◽

10.1007/s10701-021-00440-1 ◽

2021 ◽

Vol 51 (1) ◽

Author(s):

H. S. Perlman

Keyword(s):

Quantum Measurements

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Application of relativistic quantum mechanics in radial problems and E/M equations

Journal of Physics Conference Series ◽

10.1088/1742-6596/1869/1/012187 ◽

2021 ◽

Vol 1869 (1) ◽

pp. 012187

Author(s):

G Y Arygunartha ◽

N M D Janurianti ◽

Y P Situmeang

Keyword(s):

Quantum Mechanics ◽

Relativistic Quantum ◽

Relativistic Quantum Mechanics

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Quantum Euler Relation for Local Measurements

Entropy ◽

10.3390/e23070889 ◽

2021 ◽

Vol 23 (7) ◽

pp. 889

Author(s):

Akram Touil ◽

Kevin Weber ◽

Sebastian Deffner

Keyword(s):

Quantum Systems ◽

Quantum Measurements ◽

Weak Coupling Regime ◽

Local Quantum ◽

Dissipation Model ◽

Local Measurements ◽

Euler Relation ◽

Quantum Analog ◽

Back Action ◽

Classical Thermodynamics

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.

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A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Journal of High Energy Physics ◽

10.1007/jhep03(2021)076 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Ivan M. Burbano ◽

T. Rick Perche ◽

Bruno de S. L. Torres

Keyword(s):

Path Integral ◽

Degrees Of Freedom ◽

Wilson Line ◽

Transition Probability ◽

Relativistic Quantum ◽

Quantum Fields ◽

Line Defect ◽

Particle Detectors ◽

Nonlocal Operators ◽

Detector Model

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

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Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

Journal of High Energy Physics ◽

10.1007/jhep02(2021)127 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Qiang Chen ◽

Jianyuan Xiao ◽

Peifeng Fan

Keyword(s):

Field Theory ◽

Real Time ◽

Quantum Electrodynamics ◽

Symplectic Form ◽

Strong Field ◽

Relativistic Quantum ◽

High Order ◽

High Quality ◽

Geometric Structures ◽

Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

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