32 research outputs found
Exact closed master equation for Gaussian non-Markovian dynamics
Non-Markovian master equations describe general open quantum systems when no
approximation is made. We provide the exact closed master equation for the
class of Gaussian, completely positive, trace preserving, non-Markovian
dynamics. This very general result allows to investigate a vast variety of
physical systems. We show that the master equation for non-Markovian quantum
Brownian motion is a particular case of our general result. Furthermore, we
derive the master equation unraveled by a non-Markovian, dissipative stochastic
Schr\"odinger equation, paving the way for the analysis of dissipative
non-Markovian collapse models
Progress towards an effective non-Markovian description of a system interacting with a bath
We analyze a system coupled to a bath of independent harmonic oscillators. We
transform the bath in chain structure by solving an inverse eigenvalue problem.
We solve the equations of motion for the collective variables defined by this
transformation, and we derive the exact dynamics for an harmonic oscillator in
terms of the microscopic motion of the environmental modes. We compare this
approach to the well-known Generalized Langevin Equation and we show that our
dynamics satisfies this equation
Effective non-Markovian description of a system interacting with a bath
We study a harmonic system coupled to chain of first neighbor interacting
oscillators. After deriving the exact dynamics of the system, we prove that one
can effectively describe the exact dynamics by considering a suitable shorter
chain. We provide the explicit expression for such an effective dynamics and we
provide an upper bound on the error one makes considering it instead of the
dynamics of the full chain. We eventually prove how error, timescale and number
of modes in the truncated chain are related
Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules
Collapse models provide a theoretical framework for understanding how
classical world emerges from quantum mechanics. Their dynamics preserves
(practically) quantum linearity for microscopic systems, while it becomes
strongly nonlinear when moving towards macroscopic scale. The conventional
approach to test collapse models is to create spatial superpositions of
mesoscopic systems and then examine the loss of interference, while
environmental noises are engineered carefully. Here we investigate a different
approach: We study systems that naturally oscillate --creating quantum
superpositions-- and thus represent a natural case-study for testing quantum
linearity: neutrinos, neutral mesons, and chiral molecules. We will show how
spontaneous collapses affect their oscillatory behavior, and will compare them
with environmental decoherence effects. We will show that, contrary to what
previously predicted, collapse models cannot be tested with neutrinos. The
effect is stronger for neutral mesons, but still beyond experimental reach.
Instead, chiral molecules can offer promising candidates for testing collapse
models.Comment: accepted by NATURE Scientific Reports, 12 pages, 1 figures, 2 table
Possible limits on superconducting quantum computers from spontaneous wave-function collapse models
The continuous spontaneous localization (CSL) model is an alternative formulation of quantum mechanics, which introduces a noise-coupled nonlinearly to the wave function to account for its collapse. We consider CSL effects on quantum computers made of superconducting transmon qubits. As a direct effect CSL reduces quantum superpositions of the computational basis states of the qubits: we show the reduction rate to be negligibly small. However, an indirect effect of CSL, dissipation induced by the noise, also leads transmon qubits to decohere, by generating additional quasiparticles. Since the decoherence rate of transmon qubits depends on the quasiparticle density, by computing their generation rate induced by CSL, we can estimate the corresponding quasiparticle density and thus the limit set by CSL on the performances of transmon quantum computers. We show that CSL could spoil the quantum computation of practical algorithms on large devices. We further explore the possibility of testing CSL effects on superconducting devices
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.Comment: 13 pages, LaTeX, 3 figure
The effect of spontaneous collapses on neutrino oscillations
We compute the effect of collapse models on neutrino oscillations. The effect
of the collapse is to modify the evolution of the `spatial' part of the wave
function, which indirectly amounts to a change on the flavor components. In
many respects, this phenomenon is similar to neutrino propagation through
matter. For the analysis we use the mass proportional CSL model, and perform
the calculation to second order perturbation theory. As we will show, the CSL
prediction is very small - mainly due to the very small mass of neutrinos - and
practically undetectable.Comment: 24 pages, RevTeX. Updated versio
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.Comment: 13 pages, 2 figure
Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models
We provide the exact non-Markovian master equation for a two-level system interacting with a thermal bosonic bath, and we write the solution of such a master equation in terms of the Bloch vector. We show that previous approximated results are particular limits of our exact master equation. We generalize these results to more complex systems involving an arbitrary number of two-level systems coupled to different thermal baths, providing the exact master equations also for these systems. As an example of this general case we derive the master equation for the Jaynes-Cummings model
Stochastic unravelings of non-Markovian completely positive and trace-preserving maps
We consider open quantum systems with factorized initial states, providing the structure of the reduced system dynamics, in terms of environment cumulants. We show that such completely positive (CP) and trace preserving (TP) maps can be unraveled by linear stochastic Schrödinger equations (SSEs) characterized by sets of colored stochastic processes (with n-th order cumulants). We obtain both the conditions such that the SSEs provide CPTP dynamics, and those for unraveling an open system dynamics. We then focus on Gaussian non-Markovian unravellings, whose known structure displays a functional derivative. We provide a novel description that replaces the functional derivative with a recursive operatorial structure. Moreover, for the family of quadratic bosonic Hamiltonians, we are able to provide an explicit operatorial dependence for the unravelling