Topological superfluid phases of an atomic Fermi gas with in- and out-of-plane Zeeman fields and equal Rashba-Dresselhaus spin-orbit coupling

We analyze the effects of in- and out-of-plane Zeeman fields on the BCS-BEC evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves novel gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly-degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly-degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases, and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.Comment: 9 pages with 5 figures; FFLO analysis include

Stability of spin-orbit coupled Fermi gases with population imbalance

We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-BEC evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.Comment: 4+ pages with 3 figures; to appear in PR

Quantum phases of atomic Fermi gases with anisotropic spin-orbit coupling

We consider a general anisotropic spin-orbit coupling (SOC) and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.Comment: 10 pages with 7 figures; to appear in PR

Measuring the Cosmic Ray Muon-Induced Fast Neutron Spectrum by (n,p) Isotope Production Reactions in Underground Detectors

While cosmic ray muons themselves are relatively easy to veto in underground detectors, their interactions with nuclei create more insidious backgrounds via: (i) the decays of long-lived isotopes produced by muon-induced spallation reactions inside the detector, (ii) spallation reactions initiated by fast muon-induced neutrons entering from outside the detector, and (iii) nuclear recoils initiated by fast muon-induced neutrons entering from outside the detector. These backgrounds, which are difficult to veto or shield against, are very important for solar, reactor, dark matter, and other underground experiments, especially as increased sensitivity is pursued. We used fluka to calculate the production rates and spectra of all prominent secondaries produced by cosmic ray muons, in particular focusing on secondary neutrons, due to their importance. Since the neutron spectrum is steeply falling, the total neutron production rate is sensitive just to the relatively soft neutrons, and not to the fast-neutron component. We show that the neutron spectrum in the range between 10 and 100 MeV can instead be probed by the (n, p)-induced isotope production rates 12C(n, p)12B and 16O(n, p)16N in oil- and water-based detectors. The result for 12B is in good agreement with the recent KamLAND measurement. Besides testing the calculation of muon secondaries, these results are also of practical importance, since 12B (T1/2 = 20.2 ms, Q = 13.4 MeV) and 16N (T1/2 = 7.13 s, Q = 10.4 MeV) are among the dominant spallation backgrounds in these detectors

A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors

As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e., we restrict the discussion to the so called European options. Now, for a simple illustration of the relationship between true stock prices and options let us consider the following situation: if at the beginning of January the S&P index is valued at $1,277 and then at the end of December of the same year the price of the index became$1,400 then the fair price of the option to buy this in January would be $123, assuming T=1. This is a fair price because if the holder purchases the option for$122 or less then he or she gains while if the holder purchases the option for $124 or more then the bank wins while$123 is neutral for both parties. As one can see from this simple illustration predicting the fair price of an option is directly related to predicting the value of the stock price in a future time T

A Multitier Deep Learning Model for Arrhythmia Detection

Electrocardiograph (ECG) is employed as a primary tool for diagnosing cardiovascular diseases (CVD) in the hospital, which often helps in the early detection of such ailments. ECG signals provide a framework to probe the underlying properties and enhance the initial diagnosis obtained via traditional tools and patient-doctor dialogues. It provides cardiologists with inferences regarding more serious cases. Notwithstanding its proven utility, deciphering large datasets to determine appropriate information remains a challenge in ECG-based CVD diagnosis and treatment. Our study presents a deep neural network (DNN) strategy to ameliorate the aforementioned difficulties. Our strategy consists of a learning stage where classification accuracy is improved via a robust feature extraction. This is followed using a genetic algorithm (GA) process to aggregate the best combination of feature extraction and classification. The MIT-BIH Arrhythmia was employed in the validation to identify five arrhythmia categories based on the association for the advancement of medical instrumentation (AAMI) standard. The performance of the proposed technique alongside state-of-the-art in the area shows an increase of 0.94 and 0.953 in terms of average accuracy and F1 score, respectively. The proposed model could serve as an analytic module to alert users and/or medical experts when anomalies are detected in the acquired ECG data in a smart healthcare framework

Variational Quantum Linear Solver

Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum Linear Solver (VQLS), for solving linear systems on near-term quantum computers. VQLS seeks to variationally prepare $|x\rangle$ such that $A|x\rangle\propto|b\rangle$. We derive an operationally meaningful termination condition for VQLS that allows one to guarantee that a desired solution precision $\epsilon$ is achieved. Specifically, we prove that $C \geq \epsilon^2 / \kappa^2$, where $C$ is the VQLS cost function and $\kappa$ is the condition number of $A$. We present efficient quantum circuits to estimate $C$, while providing evidence for the classical hardness of its estimation. Using Rigetti's quantum computer, we successfully implement VQLS up to a problem size of $1024\times1024$. Finally, we numerically solve non-trivial problems of size up to $2^{50}\times2^{50}$. For the specific examples that we consider, we heuristically find that the time complexity of VQLS scales efficiently in $\epsilon$, $\kappa$, and the system size $N$.Comment: 13 + 8 pages, 15 figures, 7 table

Quantum Fluctuation Theorems

Recent advances in experimental techniques allow one to measure and control systems at the level of single molecules and atoms. Here gaining information about fluctuating thermodynamic quantities is crucial for understanding nonequilibrium thermodynamic behavior of small systems. To achieve this aim, stochastic thermodynamics offers a theoretical framework, and nonequilibrium equalities such as Jarzynski equality and fluctuation theorems provide key information about the fluctuating thermodynamic quantities. We review the recent progress in quantum fluctuation theorems, including the studies of Maxwell's demon which plays a crucial role in connecting thermodynamics with information.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Fundamental Aspects and New Directions", (Springer International Publishing, 2018