arXiv subjects

Angelo Bassi

Publications and source records attributed to Angelo Bassi.

At least 109 records · Page 6Linked to original sources

arXiv2012

Is quantum linear superposition an exact principle of nature?

The principle of linear superposition is a hallmark of quantum theory. It has been confirmed experimentally for photons, electrons, neutrons, atoms, for molecules having masses up to ten thousand amu, and also in collective states such as SQUIDs and Bose-Einstein condensates. However, the principle does not seem to hold for positions of large objects! Why for instance, a table is never found to be in two places at the same time? One possible explanation for the absence of macroscopic superpositions is that quantum theory is an approximation to a stochastic nonlinear theory. This hypothesis may have its fundamental origins in gravitational physics, and is being put to test by modern ongoing experiments on matter wave interferometry.

quant-ph↗

arXiv2012

Constraining CSL strength parameter $λ$ from standard cosmology and spectral distortions of CMBR

Models of spontaneous wave function collapse modify the linear Schrödinger equation of standard Quantum Mechanics by adding stochastic non-linear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such non-linear terms in the Schrödinger equation leads to non-conservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat non-relativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms on standard evolution of non-relativistic matter and on the formation of CMBR. We will use the CSL model, the most widely used collapse model. We will also put constraints on the CSL collapse rate $λ$ by considering that the standard evolution of non-relativistic matter is not hampered and the observed precise blackbody spectrum of CMBR would not get distorted (in the form of $μ-$type and $y-$type distortions) so as to violate the observed bounds.

astro-ph.CO↗

arXiv2012

Decoherence Effects on Superpositions of Chiral States in a Chiral Molecule

The superposition of chiral states of chiral molecules, as delocalized quantum states of a many-particle system, can be used for the experimental investigations of decoherence theory. In this regard, a great challenge is the precise quantification of the robustness of these superpositions against environmental effects. The methods so far proposed need the detailed specification of the internal states of the molecule, usually requiring heavy numerical calculations. Here, by using the linearized quantum Boltzmann equation and by borrowing ideas employed for analyzing other quantum systems, we present a general and simple approach, of large applicability, which can be used to compute the dominant contribution to the decoherence rate for the superpositions of chiral states of chiral molecules, due to environmental scattering.

cond-mat.stat-mech↗

arXiv2012

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schrödinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models, for infinite dimensional systems. We compute the Green's function; in the case of a free particle, and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

quant-ph↗

arXiv2011

Dissipative collapse models with non-white noises

We study the generalization of the QMUPL model which accounts both for memory and dissipative effects. This is the first model where both features are combined. After having derived the non-local Action describing the system, we solve the equation for a quantum harmonic oscillator via the path integral formalism. We give the explicit expression for the Green's function of the process. We focus on the case of an exponential correlation function and we analyze in detail the behavior Gaussian wave functions. We eventually study the collapse process, comparing the results with those of previous models.

quant-ph↗

arXiv2011

Functional Lagrange formalism for time-non-local Lagrangians

We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.

math-ph↗

arXiv2011

On the Tunneling Properties of non-Planar Molecules in a Gas Medium

We propose a simple, general, and accurate formula for analyzing the tunneling between classical configurations of a non-planar molecule in a gas medium, as a function of the thermodynamic parameters of the gas. We apply it to two interesting cases: i) The shift to zero frequency of the inversion line of ammonia, upon increase of the pressure of the gas; ii) The destruction of the coherent tunneling of D2S2 molecules in a gas of He. In both cases, we compare our analysis with previous theoretical and experimental results.

cond-mat.stat-mech↗

arXiv2010

Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks above a given scale. Theoretically, this possibility is predicted by collapse models. They provide quantitative information on where violations of the superposition principle become manifest. Here we show that the lower bound on the collapse parameter lambda, coming from the analysis of the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the original bound, in agreement with more recent analysis. This implies that the collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and thus falls within the range of testability with present-day technology. We also compare the spectrum of the collapsing field with those of known cosmological fields, showing that a typical cosmological random field can yield an efficient wave function collapse.

quant-ph↗

arXiv2009

Quantum Theory: Exact or Approximate?

Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and philosophy. There are two distinct approaches. One is to assume that quantum theory is exact, but that the interpretive postulates need modification, to eliminate apparent contradictions. The second approach is to assume that quantum mechanics is not exact, but instead is a very accurate approximation to a deeper level theory, which reconciles the deterministic and probabilistic aspects. We will focus on this second approach.

quant-ph↗

arXiv2009

On the Electromagnetic Properties of Matter in Collapse Models

We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and under only the dipole approximation, we are able to solve the equation of motion exactly. In this way, both the finite time and large time behavior can be analyzed accurately. We discovered new features, which did not appear in previous works on the same subject. Since, so far, the spontaneous photon emission process places the strongest upper bounds on the collapse parameters, our results call for a further analysis of this process for those atomic systems which can be employed in experimental tests of collapse models, as well as of quantum mechanics.

quant-ph↗

arXiv2009

Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: general solution and main properties

We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum and energy. We eventually specialize to the case of Gaussian wave functions, and prove that all basic facts about collapse models, which are known to be true in the white noise case, hold also in the more general case of non-Markovian dynamics.

quant-ph↗

arXiv2009

Non-Markovian quantum trajectories: an exact result

We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of continuous quantum measurement). For the first time, we give the explicit general solution for the free particle case (H = p^2/2m), and discuss the main properties. We analyze the case of an exponential correlation function for the noise, giving a quantitative description of the dynamics and of its dependence on the correlation time.

quant-ph↗

arXiv2009

On the long time behavior of stochastic Schroedinger evolutions

We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. Observing that there exist three time regimes, namely the collapse regime, after which the wave function is localized in space; the classical regime, during which the collapsed wave function moves along a classical path and the diffusive regime, in which diffusion overlaps significantly the deterministic motion, we study the long time behavior of the wave function. We assert that the general solution converges a.s. to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this.

quant-ph↗

arXiv2008

On the long time behavior of Hilbert space diffusion

Stochastic differential equations in Hilbert space as random nonlinear modified Schroedinger equations have achieved great attention in recent years; of particular interest is the long time behavior of their solutions. In this note we discuss the long time behavior of the solutions of the stochastic differential equation describing the time evolution of a free quantum particle subject to spontaneous collapses in space. We explain why the problem is subtle and report on a recent rigorous result, which asserts that any initial state converges almost surely to a Gaussian state having a fixed spread both in position and momentum.

quant-ph↗

arXiv2008

Collapse models with non-white noises II: particle-density coupled noises

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to a local nonrelativistic particle density. We derive general results in this model for the rates of density matrix diagonalization and of state vector reduction, and show that (in the absence of decoherence) both processes are governed by essentially the same rate parameters. As an alternative route to our reduction results, we also derive the Fokker-Planck equations that correspond to the initial stochastic Schrödinger equation. For specific models of the noise autocorrelator, including ones motivated by the structure of thermal Green's functions, we discuss the qualitative and qantitative dependence on model parameters, with particular emphasis on possible cosmological sources of the noise field.

quant-ph↗

arXiv2008

Noise gates for decoherent quantum circuits

A major problem in exploiting microscopic systems for developing a new technology based on the principles of Quantum Information is the influence of noise which tends to work against the quantum features of such systems. It becomes then crucial to understand how noise affects the evolution of quantum circuits: several techniques have been proposed among which stochastic differential equations (SDEs) can represent a very convenient tool. We show how SDEs naturally map any Markovian noise into a linear operator, which we will call a noise gate, acting on the wave function describing the state of the circuit, and we will discuss some examples. We shall see that these gates can be manipulated like any standard quantum gate, thus simplifying in certain circumstances the task of computing the overall effect of the noise at each stage of the protocol. This approach yields equivalent results to those derived from the Lindblad equation; yet, as we show, it represents a handy and fast tool for performing computations, and moreover, it allows for fast numerical simulations and generalizations to non Markovian noise. In detail we review the depolarizing channel and the generalized amplitude damping channel in terms of this noise gate formalism and show how these techniques can be applied to any quantum circuit.

quant-ph↗

arXiv2008

Collapse models with non-white noises

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the non-Schrodinger terms of the equation induce the collapse of the wave function to one of the common eigenstates of the collapsing operators, and that the collapse occurs with the correct quantum probabilities. We also develop a perturbation expansion of the solution of the equation with respect to the parameter which sets the strength of the collapse process; such an approximation allows one to compute the leading order terms for the deviations of the predictions of collapse models with respect to those of standard quantum mechanics. This analysis shows that to leading order, the ``imaginary'' noise trick can be used for non-white Gaussian noise.

quant-ph↗

arXiv2005

On the Energy Increase in Space-Collapse Models

A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature the stochastic field which is responsible for the localization mechanism causes the momentum to behave like a Brownian motion, whose larger and larger fluctuations show up as a steady increase of the energy of the system. In spite of the fact that, in all situations, such an increase is small and practically undetectable, it is an undesirable feature that the energy of physical systems is not conserved but increases constantly in time, diverging for $t \to \infty$. In this paper we show that this property of collapse models can be modified: we propose a model of spontaneous wavefunction collapse sharing all most important features of usual models but such that the energy of isolated systems reaches an asymptotic finite value instead of increasing with a steady rate.

quant-ph↗