Work fluctuations in quantum spin chains

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.Comment: 10 pages, 13 figure

Entanglement evolution after connecting finite to infinite quantum chains

We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.Comment: 15 pages, 11 figure

Quantum repeated interactions and the chaos game

Inspired by the algorithm of Barnsley's chaos game, we construct an open quantum system model based on the repeated interaction process. We shown that the quantum dynamics of the appropriate fermionic/bosonic system (in interaction with an environment) provides a physical model of the chaos game. When considering fermionic operators, we follow the system's evolution by focusing on its reduced density matrix. The system is shown to be in a Gaussian state (at all time $t$) and the average number of particles is shown to obey the chaos game equation. Considering bosonic operators, with a system initially prepared in coherent states, the evolution of the system can be tracked by investigating the dynamics of the eigenvalues of the annihilation operator. This quantity is governed by a chaos game-like equation from which different scenarios emerge.Comment: 21 pages, 8 figue

A matrix product solution for a nonequilibrium steady state of an XX chain

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from nearest neighbor z-z, are zero.Comment: 11 page

Quantum Quench from a Thermal Initial State

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor change

Activity of platinum and cetuximab in cutaneous squamous cell cancer not amenable to curative treatment

Background: Unresectable or metastatic cutaneous squamous cell cancers (cSCCs) are rare but potentially life-threatening diseases. In this setting, systemic therapy has a palliative intent with limited benefit, but there is no established consensus regarding the proper management of this tumour. This retrospective study aimed to review outcomes in patients with non-curable cSCC treated with platinum-based chemotherapy and cetuximab. Methods: We considered 12 consecutive patients treated between June 2010 and March 2016. All patients had received previous treatment for the local disease. Results: The overall response rate was 50%, and the disease control rate was 67%. Median progression-free survival and overall survival were 6.6 (95% confidence interval [CI]: 1.9-8.4) and 14.6 (95% CI: 9.4-20.1) months, respectively. The median duration of response was 4.8 months (95% CI: 1.2-5.9). The most frequent toxicities were skin reactions (58%; grade 3: 25%) and anaemia (10%). No grade 4 toxicities were observed. Conclusions: Cetuximab and platinum-based chemotherapy were shown to be feasible and active in cSCC, with an acceptable toxicity profile, even if with a limited duration of response

Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?

We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain-wall. We generalize the path-integral imaginary time approach that together with boundary conformal field theory allows to derive the time and space dependence of general correlation functions. The latter are explicitly obtained for the Ising universality class, and the typical behavior of one- and two-point functions is derived for the general case. Possible connections with the stochastic Loewner evolution are discussed and explicit results for one-point time dependent averages are obtained for generic \kappa for boundary conditions corresponding to SLE. We use this set of results to predict the time evolution of the entanglement entropy and obtain the universal constant shift due to the presence of a domain wall in the initial state.Comment: 27 pages, 10 figure

Entanglement and correlation functions following a local quench: a conformal field theory approach

We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bi-partitions of the line. We also consider the behavior of one- and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid more generally, whereby quasiparticles emitted from the joining point at the initial time propagate semiclassically through the system.Comment: 19 pages, 4 figures, v2 typos corrected and refs adde

Entanglement in spin chains with gradients

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the transverse Ising chain. We explain this behaviour and indicate generalizations to other power laws.Comment: 16 pages, 11 figures, 2 references adde