Quantum Break Time Research Articles

When quantum corrections alter the predictions of classical field theory for scalar field dark matter

We investigate the timescale on which quantum corrections alter the predictions of classical field theory for scalar field dark matter. This is accomplished by including second order terms in the evolution proportional to the covariance of the field operators. When this covariance is no longer small compared to the mean field value, we say that the system has reached the ``quantum breaktime" and the predictions of classical field theory will begin to differ from those of the full quantum theory. While holding the classical field theory evolution fixed, we determine the change of the quantum breaktime as total occupation number is increased. This provides a novel numerical estimation of the breaktime based at high occupations $n_{tot}$ and mode number $N=256$. We study the collapse of a sinusoidal overdensity in a single spatial dimension. We find that the breaktime scales as $\log(n_{tot})$ prior to shell crossing and then then as a powerlaw following the collapse. If we assume that the collapsing phase is representative of halos undergoing nonlinear growth, this implies that the quantum breaktime of typical systems may be as large as $\sim 30$ of dynamical times even at occupations of $n_{tot}\sim 10^{100}$.

Breaking BEC: Quantum evolution of unstable condensates

In this work we numerically explore the quantum behavior of a classically unstable relativistic Bose-Einstein condensate (BEC). The main goal is to study the phenomenon of so-called quantum break time which amounts to a significant departure from a semiclassical mean-field description. It has been suggested previously that the existence of Lyapunov instability is crucial for a fast quantum breaking, chaos, and scrambling. In order to clarify the issue, we work within the 2-PI effective action formalism and introduce a simple and very widely applicable dynamical criterion for identifying the timescale of quantumbreaking. We indeed observe that the fast quantum break time is controlled by the Lyapunov exponent of the unstable BEC.

Single classical field description of interacting scalar fields

We test the degree to which interacting Bosonic systems can be approximated by a classical field as total occupation number is increased. This is done with our publicly available code repository, QIBS, a new massively parallel solver for these systems. We use a number of toy models well studied in the literature and track when the classical field description admits quantum corrections, called the quantum breaktime. This allows us to test claims in the literature regarding the rate of convergence of these systems to the classical evolution. We test a number of initial conditions, including coherent states, number eigenstates, and field number states. We find that of these initial conditions, only number eigenstates do not converge to the classical evolution as occupation number is increased. We find that systems most similar to scalar field dark matter exhibit a logarithmic enhancement in the quantum breaktime with total occupation number. Systems with contact interactions or with field number state initial conditions, and linear dispersions, exhibit a power law enhancement. Finally, we find that the breaktime scaling depends on both model interactions and initial conditions.

Swampland conjectures for an almost topological gravity theory

We analyze AdS and dS swampland conjectures in a three-dimensional higher spin theory with self-interacting matter, which contains conformal gravity and is almost topological. A theory of a similar type was proposed as the effective theory in the high energy phase of non-critical M-theory in 3D. With some details differing from the usual string theory story, it is found that the resulting effective theory, namely topologically massive gravity, fits well into the web of the proposed swampland conjectures. Supporting a recent proposal, in particular we find that this 3D theory gives rise to a quantum break time that scales like tQ∼H−1.

Bounds on quantum information storage and retrieval.

We present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein-Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole, this reproduces the Page time as well as the quantum break-time. Again, the expression for the information retrieval time is very general and is shared by non-gravitational saturated states in gauge theories including QCD. All such objects exhibit universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems. This article is part of the theme issue 'Quantum technologies in particle physics'.

Field moment expansion method for interacting bosonic systems

We introduce a numerical method and python package, https://github.com/andillio/CHiMES, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum breaktime of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting Bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and that the growth of the higher order moments be hierarchical.

De Sitter quantum breaking, swampland conjectures and thermal strings

We argue that under certain assumptions the quantum break time approach and the trans-Planckian censorship conjecture both lead to de Sitter swampland constraints of the same functional form. It is a well known fact that the quantum energy-momentum tensor in the Bunch-Davies vacuum computed in the static patch of dS breaks some of the isometries. Proposing that this is a manifestation of quantum breaking of dS, we analyze some of its consequences. In particular, this leads to a thermal matter component that can be generalized to string theory in an obvious way. Imposing a censorship of quantum breaking, we recover the no eternal inflation bound in the low temperature regime, while the stronger bound from the dS swampland conjecture follows under a few reasonable assumptions about the still mysterious, presumably topological, high-temperature regime of string theory.

S-Matrix and Anomaly of de Sitter

S-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The S-matrix constraint is enforced by an anomalous quantum break-time proportional to the inverse values of gravitational and/or string couplings. Due to this, de Sitter can satisfy the conditions for a valid vacuum only at the expense of trivializing the graviton and closed-string S-matrices. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular 1/N effects, similarly to Witten–Veneziano mechanism in QCD with N colors. In this picture, an S-matrix formulation of Einstein gravity, such as string theory, nullifies an outstanding cosmological puzzle. We discuss possible observational signatures which are especially interesting in theories with a large number of particle species. Species can enhance the primordial quantum imprints to potentially observable level even if the standard inflaton fluctuations are negligible.

Breaking BEC

In this work quantum corrections to the classical evolution of a relativistic scalar condensate are studied. The problem is approached by means of two different perturbative approaches: the 2-particle-irreducible (2PI) effective action and the expansion in the self-coupling. In the weak coupling regime the decoherence of the classical state is observed. The corresponding timescale is identified with the quantum break-time.

Universe's primordial quantum memories

We provide a very general argument showing that the Universe must have kept its quantum memories from an epoch much earlier than 60 e-foldings before the end of inflation. The point is that a generic system of enhanced memory storage capacity exhibits a phenomenon of memory burden. Due to its universal nature this effect must be applicable to de Sitter since the latter has a maximal memory storage capacity thanks to its Gibbons-Hawking entropy. The primordial information pattern encoded in de Sitter memory initially costs very little energy. However, because of Gibbons-Hawking evaporation, the memory burden of the pattern grows in time and increasingly back reacts on the evaporation process. After a finite time the memory burden becomes unbearable and de Sitter quantum breaks. If inflation ended not long before its quantum break-time, the imprints of the primordial memory pattern can be observable. This provides a qualitatively new type of window in the Universe's beginning, a sort of cosmic quantum hair.

On Exclusion of Positive Cosmological Constant

AbstractSome time ago we have suggested that positive vacuum energy exhibits a finite quantum break time, which can be a signal that a positive cosmological constant is inconsistent. From the requirement that the Universe never undergoes through quantum breaking, we have derived an absolute lower bound on the speed of variation of positive vacuum energy. The same suggestion about exclusion of positive cosmological constant was made recently. We show that the new bound represents a particular string theoretic version of the old bound, which is more general. In this light, we show that the existing window still provides a large room for the inflationary and dark energy model building. In particular, the inflationary models with gravitational strength interactions, are protected against fast quantum breaking.

Classicality and quantum break-time for cosmic axions

We investigate the length of the period of validity of a classical description for the cosmic axion field. To this end, we first show that we can understand the oscillating axion solution as expectation value over an underlying coherent quantum state. Once we include self-interaction of the axion, the quantum state evolves so that the expectation value over it starts to deviate from the classical solution. The time-scale of this process defines the quantum break-time. For the hypothetical dark matter axion field in our Universe, we show that quantum break-time exceeds the age of the Universe by many orders of magnitude. This conclusion is independent of specific properties of the axion model. Thus, experimental searches based on the classical approximation of the oscillating cosmic axion field are fully justified. Additionally, we point out that the distinction of classical nonlinearities and true quantum effects is crucial for calculating the quantum break-time in any system. Our analysis can also be applied to other types of dark matter that are described as classical fluids in the mean field approximation.

Semiclassical theory of strong localization for quantum thermalization.

We introduce a semiclassical theory for strong localization that may arise in the context of many-body thermalization. As a minimal model for thermalization we consider a few-site Bose-Hubbard model consisting of two weakly interacting subsystems that can exchange particles. The occupation of a subsystem (x) satisfies in the classical treatment a Fokker-Planck equation with a diffusion coefficient D(x). We demonstrate that it is possible to deduce from the classical description a quantum breaktime t^{*} and, hence, the manifestations of a strong localization effect. For this purpose it is essential to take the geometry of the energy shell into account and to make a distinction between different notions of phase-space exploration.

Quantum break-time of de Sitter

The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background—e.g., in terms of a coherent state—is required. In this paper, we first consider a simple scalar model with anharmonic oscillations and derive its quantum break-time. Next, following [1], we apply these ideas to de Sitter space. We formulate a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as quantum coherent state of gravitons. The mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all the known properties of de Sitter, such as the redshift of probe particles and thermal Gibbons-Hawking radiation, all in the language of quantum S-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the 1/N-effects to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10100 years old in its entire classical history.

Barrier-induced chaos in a kicked rotor: Classical subdiffusion and quantum localization.

The relation between classically chaotic dynamics and quantum localization is studied in a system that violates the assumptions of the Kolmogorov-Arnold-Moser (KAM) theorem, namely, the kicked rotor in a discontinuous potential barrier. We show that the discontinuous barrier induces chaos and more than two distinct subdiffusive energy growth regimes, the latter being an unusual feature for Hamiltonian chaos. We show that the dynamical localization in the quantized version of this system carries the imprint of non-KAM classical dynamics through the dependence of quantum break time on subdiffusion exponents. We briefly comment on the experimental feasibility of this system.

Scrambling in the black hole portrait

Recently a quantum portrait of black holes was suggested according to which a macroscopic black hole is a Bose-Einstein condensate of soft gravitons stuck at the critical point of a quantum phase transition. We explain why quantum criticality and instability are the key for efficient generation of entanglement and consequently of the scrambling of information. By studying a simple Bose-Einstein prototype, we show that the scrambling time, which is set by the quantum break time of the system, goes as $\log N \,$ for $N$ the number of quantum constituents or equivalently the black hole entropy.

Influence of experimental resolution on the quantum-to-classical transition in the quartic oscillator

The quantum-classical transition problem is investigated for the quartic oscillator coupled to a thermal reservoir. We show for this model that the combination of relevant diffusion, classical action (represented by the amplitude of an initial coherent state) and the experimental uncertainties is necessary to achieve the classical regime. In order to study the role of limited resolutions of measurement apparatuses on the correspondence between the quantum and classical dynamics, we consider experimental errors due the preparation of the initial state of the quartic oscillator and the inaccuracies in the time measurements. A quantum break time depending on the diffusion constant, the amplitude of the initial coherent state and the inaccuracy of measurements is defined. We found, for this model, a regime where the increasing of diffusion does not anticipate classicality. In such regime, there is a minimum value for the classical action associated to classical behavior of the system.

Chaotic Hamiltonian ratchets for pulsed periodic double-well potentials: Classical correlations and the ratchet current

We present analytical derivations of the diffusion rates, ratchet currents, and time scales of a new ratchet in a fully chaotic Hamiltonian system, introduced in Phys. Rev. Lett. 89, 194102 (2002)] with a proposed implementation using atoms in pulsed standing waves of light. The origin of this type of ratchet current is in asymmetric momentum diffusion rates which result when a "double-well" lattice is pulsed with unequal "kick" periods. The form of the new short-time correlations which modify the diffusion rates are derived. The resulting formulas for the classical energy diffusion rates are shown to give good agreement with numerical simulations. A closed analytical formula for the ratchet current is also obtained, which predicts correctly the current magnitudes and current reversals. The characteristic "ratchet time," a classical time scale associated with the momentum-diffusion ratchet is derived analytically. The competition between the ratchet time t(r) , and the quantum break time t(*) is investigated further.

Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory

We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity of a mean-field dynamical instability. Convergence to mean-field theory (MFT), with increasing total number of particles $N$, is shown to be logarithmically slow. Using a density matrix formalism rather than the conventional wavefunction methods, we derive an improved set of equations of motion for the mean-field plus the fluctuations, which goes beyond MFT and provides accurate predictions for the leading quantum corrections and the quantum break time. We show that the leading quantum corrections appear as decoherence of the reduced single-particle quantum state; we also compare this phenomenon to the effects of thermal noise. Using the rapid dephasing near an instability, we propose a method for the direct measurement of scattering lengths.

Bose-Einstein condensates beyond mean field theory: quantum backreaction as decoherence.

We propose an experiment to measure the slow log(N) convergence to mean field theory (MFT) around a dynamical instability. Using a density matrix formalism instead of the standard macroscopic wave function approach, we derive equations of motion which go beyond MFT and provide accurate predictions for the quantum break time. The leading quantum corrections appear as decoherence of the reduced single-particle quantum state.