arXiv subjects

Antoine Tilloy

Publications and source records attributed to Antoine Tilloy.

At least 37 records · Page 2Linked to original sources

arXiv2021

Variational method in relativistic quantum field theory without cutoff

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.

quant-ph↗

arXiv2020

Arbitrarily large neutron amplification in subcritical nuclear reactors

In a subcritical reactor, each neutron produces only keff < 1 neutron per generation (asymptotically and on average), and thus the neutron population decreases exponentially in the absence of external source. The chain reaction is thus easy to stop, making such reactors inherently stable. Interestingly, and contrary to common wisdom, there is no relation between keff, the external source intensity, and the output power of the reactor. In this paper, I present various possible strategies to exploit this fact, and apply them to the design of a rudimentary multi-layer system that allows to reach an arbitrarily large number of fissions per source neutron, while keeping keff < 1 fixed (I used keff=0.97). The behavior of the amplifier is verified with simple Monte-Carlo transport simulations. The proposal admittedly brings complications and subtleties that need to be studied further, but, if developed, could allow to drive subcritical reactors with faint neutron sources, e.g. radioisotope based.

physics.ins-det↗

arXiv2020

The subtle sound of quantum jumps

Could we hear the pop of a wave-function collapse, and if so, what would it sound like? There exist reconstructions or modifications of quantum mechanics (collapse models) where this archetypal signature of randomness exists and can in principle be witnessed. But, perhaps surprisingly, the resulting sound is disappointingly banal, indistinguishable from any other click. The problem of finding the right description of the world between two completely different classes of models -- where wave functions jump and where they do not -- is empirically undecidable. Behind this seemingly trivial observation lie deep lessons about the rigidity of quantum mechanics, the difficulty to blame unpredictability on intrinsic randomness, and more generally the physical limitations to our knowledge of reality.

quant-ph↗

arXiv2020

Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories

Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper, we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians, and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow to renormalize away simple divergences variationally. In the end, our study makes it plausible that CTNSs are indeed a good manifold to approximate the low energy states of QFTs.

cond-mat.str-el↗

arXiv2020

Computing the renormalization group flow of two-dimensional $ϕ^4$ theory with tensor networks

We study the renormalization group flow of $ϕ^4$ theory in two dimensions. Regularizing space into a fine-grained lattice and discretizing the scalar field in a controlled way, we rewrite the partition function of the theory as a tensor network. Combining local truncations and a standard coarse-graining scheme, we obtain the renormalization group flow of the theory as a map in a space of tensors. Aside from qualitative insights, we verify the scaling dimensions at criticality and extrapolate the critical coupling constant $f_{\rm c} = λ/ μ^2$ to the continuum to find $f^{\rm cont.}_{\rm c} = 11.0861(90)$, which favorably compares with alternative methods.

cond-mat.str-el↗

arXiv2019

Continuous collapse models on finite dimensional Hilbert spaces

We review recent results on the dynamics of continuous collapse models (or equivalently continuous measurement models) on finite dimensional Hilbert spaces. We mainly study the pure collapse dynamics, and the competition between collapse and unitary or Lindbladian dynamics. We discuss the ubiquitous emergence of quantum jumps from a continuous stochastic evolution when collapse dominates, and expand on a finer unexpected feature, the quantum spikes.

quant-ph↗

arXiv2019

Neutron star heating constraints on wave-function collapse models

Spontaneous wavefunction collapse models, like the Continuous Spontaneous Localization, are designed to suppress macroscopic superpositions, while preserving microscopic quantum phenomena. An observable consequence of collapse models is spontaneous heating of massive objects. Here we calculate the collapse-induced heating rate of astrophysical objects, and the corresponding equilibrium temperature. We apply these results to neutron stars, the densest phase of baryonic matter in the universe. Stronger collapse model parameters imply greater heating, allowing us to derive competitive bounds on model parameters using neutron star observational data, and to propose speculative bounds based on the capabilities of current and future astronomical surveys.

quant-ph↗

arXiv2019

Entanglement in a fermion chain under continuous monitoring

We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

cond-mat.stat-mech↗

arXiv2019

Continuous Tensor Network States for Quantum Fields

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending Projected Entangled Pair States (PEPS), we propose a generalization bearing similarities with the continuum Multi-scale Entanglement Renormalization Ansatz (cMERA).

cond-mat.str-el↗

arXiv2019

Does gravity have to be quantized? Lessons from non-relativistic toy models

It is often argued that gravity has to be a quantum theory simply because a fundamentally semiclassical approach would necessarily be inconsistent. Here I review recent Newtonian toy models of (stochastic) semiclassical gravity. They provide one option to implement a force semiclassically without getting into the known problems associated with mean-field. These models are not complete theories and should not be considered too seriously, but their consistency shows that semiclassical gravity is hard to dismiss on purely theoretical grounds.

quant-ph↗

arXiv2018

Exact signal correlators in continuous quantum measurements

This article provides an exact formula for the signal n-point correlation functions of detectors continuously measuring an arbitrary quantum system, in the presence of detection imperfections. The derivation uses only continuous stochastic calculus techniques, but the final result is easily understood from a discrete picture of repeated interactions with qubits or from a parallel with continuous matrix product states. This result provides a crude yet efficient a way to estimate system parameters directly from experimental data, without requiring non-linear state reconstruction.

quant-ph↗

arXiv2018

Binding quantum matter and space-time, without romanticism

Understanding the emergence of a tangible 4-dimensional space-time from a quantum theory of gravity promises to be a tremendously difficult task. This article makes the case that this task may not have to be carried. Space-time as we know it may be fundamental to begin with. I recall the common arguments against this possibility and review a class of recently discovered models bypassing the most serious objection. The generic solution of the measurement problem that is tied to semiclassical gravity as well as the difficulty of the alternative make it a reasonable default option in the absence of decisive experimental evidence.

physics.hist-ph↗

arXiv2018

Ghirardi-Rimini-Weber model with massive flashes

I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or collapse space-time events) source a classical gravitational field. The resulting semi-classical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the $1/r$ gravitational potential of Newtonian gravity is cut-off at short ($\lesssim 10^{-7}$m) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for \emph{all} values of its parameters.

quant-ph↗

arXiv2017

Comment on "Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems"

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter $θ(0)$ is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way and finally shows where the main mistake of the authors of the original article was made.

quant-ph↗

arXiv2017

On GKLS dynamics for local operations and classical communication

We define a time continuous version of the concept of "local operations and classical communication" (LOCC), ubiquitous in quantum information theory. It allows us to construct GKLS master equations for particle systems that have (1) an arbitrary pair potential, and (2) local decoherence terms, but that do not entangle the constituents. The local decoherence terms take a particularly simple form if a principle of least decoherence is applied.

quant-ph↗

arXiv2017

Time-local unraveling of non-Markovian stochastic Schrödinger equations

Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.

quant-ph↗

arXiv2017

Principle of least decoherence for Newtonian semi-classical gravity

Recent works have proved that semi-classical theories of gravity needed not be fundamentally inconsistent, at least in the Newtonian regime. Using the machinery of continuous measurement theory and feedback, it was shown that one could construct well behaved models of hybrid quantum-classical dynamics at the price of an imposed (non unique) decoherence structure. We introduce a principle of least decoherence (PLD) which allows to naturally single out a unique model from all the available options; up to some unspecified short distance regularization scale. Interestingly, the resulting model is found to coincide with the old --erstwhile only heuristically motivated-- proposal of Penrose and one of us for gravity-related spontaneous decoherence and collapse. Finally, this letter suggests that it is in the submillimeter behavior of gravity that new phenomena might be found.

quant-ph↗

arXiv2017

Interacting quantum field theories as relativistic statistical field theories of local beables

We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem. Additionally, it relaxes structural constraints on standard QFTs and hence might open the way to future mathematically rigorous constructions as well as new numerical methods. Finally, because it shows that collapse models can be hidden within QFTs, this article calls for a reconsideration of the dynamical program, as a possible underpinning rather than as a modification of quantum theory.

quant-ph↗