scholarly journals Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Oleksandr Gamayun ◽  
Oleg Lychkovskiy ◽  
Jean-Sébastien Caux
Keyword(s):  
Entanglement Entropy ◽  
Bound State ◽  
Initial State ◽  
Fredholm Determinants ◽  
One Dimensional ◽  
Opposite Case ◽  
Full Counting Statistics ◽  
Loschmidt Echo ◽  
Counting Statistics ◽  
The Right

We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

scholarly journals Full Counting Statistics of Laser Excited Rydberg Aggregates in a One-Dimensional Geometry

2014 ◽  
Vol 112 (1) ◽  
Author(s):  
H. Schempp ◽  
G. Günter ◽  
M. Robert-de-Saint-Vincent ◽  
C. S. Hofmann ◽  
D. Breyel ◽  
...  
Keyword(s):  
One Dimensional ◽  
Full Counting Statistics ◽  
Counting Statistics

scholarly journals Exact thermal properties of free-fermionic spin chains

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Białończyk ◽  
Fernando Gómez-Ruiz ◽  
Adolfo del Campo
Keyword(s):  
Algebraic Approach ◽  
Transverse Field ◽  
Spin Chains ◽  
One Dimensional ◽  
Thermal Distribution ◽  
Full Counting Statistics ◽  
Integrable Spin ◽  
Counting Statistics ◽  
Integrable Spin Chains ◽  
The One

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

scholarly journals A Model of a Quantum Particle in a Quantum Environment: A Numerical Study

2015 ◽  
Vol 18 (1) ◽  
pp. 247-262 ◽  
Author(s):  
Raffaele Carlone ◽  
Rodolfo Figari ◽  
Claudia Negulescu
Keyword(s):  
Quantum Particle ◽  
Numerical Study ◽  
Spherical Wave ◽  
Classical Trajectory ◽  
Cloud Chamber ◽  
Superposition State ◽  
Initial State ◽  
One Dimensional ◽  
Average Momentum ◽  
The Right

AbstractWe define and investigate, via numerical analysis, a one dimensional toy-model of a cloud chamber. An energetic quantum particle, whose initial state is a superposition of two identical wave packets with opposite average momentum, interacts during its evolution and exchanges (small amounts of) energy with an array of localized spins. Triggered by the interaction with the environment, the initial superposition state turns into an incoherent sum of two states describing the following situation: or the particle is going to the left and a large number of spins on the left side changed their states, or the same is happening on the right side. This evolution is reminiscent of what happens in a cloud chamber where a quantum particle, emitted as a spherical wave by a radioactive source, marks its passage inside a supersaturated vapour-chamber in the form of a sequence of small liquid bubbles arranging themselves around a possible classical trajectory of the particle.

scholarly journals Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Giacomo De Palma ◽  
Lucas Hackl
Keyword(s):  
Entanglement Entropy ◽  
Quantum Systems ◽  
Von Neumann Entropy ◽  
Classical Dynamics ◽  
Initial State ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Periodically Driven ◽  
Initial States ◽  
The Right

We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models.

scholarly journals Full counting statistics of spin-flip and spin-conserving charge transitions in Pauli-spin blockade

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Sadashige Matsuo ◽  
Kazuyuki Kuroyama ◽  
Shunsuke Yabunaka ◽  
Sascha R. Valentin ◽  
Arne Ludwig ◽  
...  
Keyword(s):  
Spin Flip ◽  
Full Counting Statistics ◽  
Spin Blockade ◽  
Counting Statistics
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