A new formalism will be presented in order to study real time evolution of quantum systems at finite temperature. Probability distributions for time-correlated observables will be studied non-perturbatively and fully quantized. This works for various systems, including ones with tunneling phenomena. We have obtained good results with some computational methods which can be used on models with several degrees of freedom. Thus it looks feasible to study vacuum tunneling in real time for relevant field theories at finite T. 1.
A new formalism will be presented in order to study real time evolution of quantum systems at finite temperature. Probability distributions for time-correlated observables will be studied non-perturbatively and fully quantized. This works for various systems, including ones with tunneling phenomena. We have obtained good results with some computational methods which can be used on models with several degrees of freedom. Thus it looks feasible to study vacuum tunneling in real time for relevant field theories at finite T. 1.
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check selfconsistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable. 1 1
This book provides a comprehensive and pedagogical account of the various methods used in the quantum theory of finite systems, including molecular, atomic, nuclear, and particle phenomena. Covering both background material and advanced topics and including nearly 200 problems, Quantum Theory of Finite Systems has been designed to serve primarily as a text and will also prove useful as a reference in research.The first of the book's four parts introduces the basic mathematical apparatus: second quantization, canonical transformations, Wick theorems and the resulting diagram expansions, and oscillator models. The second part presents mean field approximations and the recently developed path integral methods for the quantization of collective modes. Part three develops perturbation theory in terms of both time-dependent Feynman diagrams and time-independent Goldstone diagrams. A fourth part discusses variational methods based on correlated wavefunctions, including spin correlations. The approximation schemes are formulated for fermions and bosons at eigher zero or non-zero temperature.Although the formalism developed applies to both finite and infinite systems, the book stresses those aspects of the theory that are specific to the description of finite systems. Thus special attention is given to mean field approximations, the ensuing broken symmetries, and the associated collective motions such as rotations. Conversely, some specific features of systems with infinite numbers of degrees of freedom (such as the thermodynamic limit, critical phenomena, and the elimination of ultraviolet divergencies) are deliberately omitted.Jean-Paul Blaizot and Georges Ripka are associated with the Centre d'Etudes Nucleaires de Saclay.
We now start what will be the subject of this book: quantum field theory at non-zero temperature and/or non-zero chemical potential. Two competing formalisms have been used at zero temperature in order to study field theory: the operator formalism, which is the older one, and the path integral formalism, which represents the more modern approach. Actually, it may often be illuminating to look at a given problem from both points of view, although in some cases one of the formalisms may prove to be definitely superior to the other: for example, path integrals are much simpler when quantizing gauge theories. At finite temperature, both formalisms are useful, and it is instructive to be able to switch from one approach to the other. Since the simplest case of field theory is field theory with zero space dimension, or, in other words, quantum mechanics, we shall begin with a short description of quantum mechanics at finite temperature, or, equivalently, quantum statistical mechanics. We first deal with the path integral approach, and later on revert to the more conventional operator formalism. We shall be particularly interested in time-ordered products of position operators, which will generalize to time-ordered products of field operators in field theory.
We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and/or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing ``causal'' field superoperators using the fundamental physical principles of causality/probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time evolution is renormalized by explicitly performing the wideband limit on the superoperator level. As a result, the occurrence of destruction and creation superoperators are shown to be tightly linked to the physical short- and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time. (ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading-order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization. (iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli-principle also simplifies problems with nonzero Coulomb interaction.
We design and implement a quantum annealing simulation platform to observe and study dynamical processes in quantum field theory (QFT). Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof of concept, we encode a scalar field theory and measure the probability for it to tunnel from the false vacuum to the true vacuum for various tunneling times, vacuum displacements, and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a promising platform for encoding QFTs. This is the first time it has been possible to measure instanton processes across a freely chosen QFT energy barrier. We argue that this novel and flexible method to study the dynamics of quantum systems has potential application to many field theories of interest. Measurements of the dynamical behavior of such encoded field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. Soon, measurements using such a quantum annealing simulation platform could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.