We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the particle production though being reversible in time. We associate this state a non-dissipative classical fluctuations and study their trigger to develop the coherent state which can be classical if sufficiently developed. The Schwinger-Keldysh in-in formalism yields the classical Langevin equation including the fluctuation force which faithfully reflects the particle production property of the original quantum system. This formalism is applied to some transient process; the initiation of the spontaneous symmetry breaking, appearance of the off-diagonal long-range order in Bose-Einstein condensation, a transient process of the classicalization of the quantum fluctuations in the inflationary cosmology,... and gives some implications on the origin of the irreversibility associated with the transition from quantum to classical.
We explore the transient dynamics associated with the emergence of the classical signal in the full quantum system. We start our study from the instability which promotes the squeezing of the quantum system. This is often interpreted as the particle production though being reversible in time. We associate this state a non-dissipative classical fluctuations and study their trigger to develop the coherent state which can be classical if sufficiently developed. The Schwinger-Keldysh in-in formalism yields the classical Langevin equation including the fluctuation force which faithfully reflects the particle production property of the original quantum system. This formalism is applied to some transient process; the initiation of the spontaneous symmetry breaking, appearance of the off-diagonal long-range order in Bose-Einstein condensation, a transient process of the classicalization of the quantum fluctuations in the inflationary cosmology,... and gives some implications on the origin of the irreversibility associated with the transition from quantum to classical.
Many quantum systems in various fields, a classical signal spontaneously appears without any specific operations/measurements. For example, the initiation of the spontaneous symmetry breaking, the appearance of the off-diagonal long-range order in the Bose-Einstein condensate, the transient process of the quantum fluctuations in the early Universe, etc. We are interested in the basic principle of these transient processes in quantum systems which shows classical signal spontaneously. We start our observation that some instability often promotes the squeezing of the original quantum system. This is usually interpreted as the particle production or the Bogoliubov shift of the vacuum. At this stage, everything is Unitary and reversible. For example, Hawking radiation around the Black Hole, the thermal state associated with the accelerated observer (Unruh effect), and the particle production in the expanding universe, etc. are all in this category. By using the Schwinger-Keldysh in-in formalism of quantum field theory, we find that these squeezed states are associated with non-dissipative classical fluctuations. We call them dry-noise. Then applying the generalized effective action method and deriving the Langevin equation, we find that these dry-noise triggers, through nonlinear interactions, to develop the coherent state which can be classical if sufficiently developed. This is the origin of the classical signal in the full quantum systems. The appearance of the squeezed state through the tachyonic instability and the development of the coherent state through the nonlinearity seem to be a general transient process that a classical signal spontaneously develops. These states appear more generally not only in the quantum optics. We finally show that this formalism is widely applicable; initiation dynamics of the spontaneous symmetry breaking in quantum systems such as BEC, Black hole entropy, Unruh detectors, and quantum cosmology. These analyses may give some implications on the origin of the irreversibility associated with the transition from quantum to classical. The detail description is in arxiv.org/abs/1810.11293 and the references therein.
We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.
The question of whether Bose-Einstein condensation involves spontaneous symmetry breaking is surprisingly controversial. We review the theory of spontaneous symmetry breaking in ferromagnets, compare it with the theory of symmetry breaking in condensates, and discuss the different viewpoints on the correspondence to experiments. These viewpoints include alternative perspectives in which we can treat condensates with fixed particle numbers, and where coherence arises from measurements. This question relates to whether condensates of quasiparticles such as polaritons can be viewed as “real” condensates. Introduction Spontaneous symmetry breaking is a deep subject in physics with long historical roots. At the most basic level, it arises in the field of cosmology. Physicists have long had an aesthetic principle that leads us to expect symmetry in the all of the basic equations of physical law. Yet the universe is manifestly full of asymmetries. How does a symmetric system acquire asymmetry merely by evolving in time? Starting in the 1950s, cosmologists began to borrow the ideas of spontaneous symmetry breaking from condensed matter physics, which were originally developed to explain spontaneous magnetization in ferromagnetic systems. Spontaneous coherence in all its forms (e.g., Bose-Einstein condensation [BEC], superconductivity, and lasing) can be viewed as another type of symmetry breaking. The Hamiltonian of the system is symmetric, yet under some conditions, the energy of the system can be reduced by putting the system into a state with asymmetry, namely, a state with a common phase for a macroscopic number of particles. The symmetry of the system implies that it does not matter what the exact choice of that phase is, as long as it is the same for all the particles. It is not obvious, however, whether the symmetry breaking which occurs in spontaneous coherence of the type seen in lasers or in Bose-Einstein condensation is the same as that seen in ferromagnetic systems. There are similarities in the systems which encourage the same view of all types of symmetry breaking, but there are also differences. In fact, there is a substantial school of thought that symmetry breaking in Bose-Einstein condensates with ultracold atoms is a “convenient fiction” (a term applied to optical coherence by Mølmer [1]).
Abstract We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.
We study nonequilibrium cascades in which fragile bound or coherent structures are formed through intermediate states rather than by direct equilibration. Motivated by light-nuclei production in relativistic heavy-ion collisions and by Bose--Einstein condensation in cosmological settings, we analyze such processes within the Schwinger--Keldysh real-time formalism. We show that commonly used rate equations can be understood as a controlled Markovian approximation obtained by integrating out intermediate reservoirs in an underlying multi-component nonequilibrium dynamics. When the finite lifetime of these reservoirs is retained, non-Markovian memory effects naturally appear, leading to delayed and history-dependent formation dynamics. The associated memory time provides a quantitative criterion for the validity of reduced, rate-based descriptions far from equilibrium.
Extended quantum systems can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently describes both dynamical and static properties. We show here that in thermal equilibrium, defined by the validity of fluctuation-dissipation relations, the action of a quantum system is invariant under a certain symmetry transformation, and thus it is distinguished from generic systems. In turn, the fluctuation-dissipation relations can be derived as the Ward-Takahashi identities associated with this symmetry. Accordingly, the latter provides an efficient test for the onset of thermodynamic equilibrium and it makes checking the validity of fluctuation-dissipation relations unnecessary. In the classical limit, this symmetry reduces to the well-known one that characterizes equilibrium in the stochastic dynamics of classical systems coupled to thermal baths, described by Langevin equations.