Universality of Internal Correlations of Strongly Interacting p-Wave Fermions in One-Dimensional Geometry.

We consider the many-body ground state of polarized fermions interacting via zero-range p-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order reduced density matrix describing arbitrary subsystem are completely independent of the shape of an external potential. It means that quantum correlations between any two subsystems are in this limit insensitive to the confinement. In addition, we show that the purity of these matrices quantifying the amount of quantum correlations can be obtained analytically for any number of particles without diagonalizing them. This observation may serve as a rigorous benchmark for other models and methods describing strongly interacting p-wave fermions.

Sudden quench of harmonically trapped mass-imbalanced fermions.

Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.

Unconventional pairing in few-fermion systems at finite temperature.

Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations-quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde-Ferrel-Larkin-Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.

Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential.

We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

One-dimensional mixtures of several ultracold atoms: a review.

Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap.

Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtained solutions to higher dimensions.

Simulating polaron biophysics with Rydberg atoms.

Transport of excitations along proteins can be formulated in a quantum physics context, based on the periodicity and vibrational modes of the structures. Numerically exact solutions of the corresponding equations are very challenging to obtain on classical computers. Approximate solutions based on the Davydov ansatz have demonstrated the possibility of stabilized solitonic excitations along the protein, however, experimentally these solutions have never been directly observed. Here we propose an alternative study of biophysical transport phenomena based on a quantum simulator composed of a chain of ultracold dressed Rydberg atoms, which allows for a direct observation of the Davydov phenomena. We show that there is an experimentally accessible range of parameters where the system directly mimics the Davydov equations and their solutions. Moreover, we show that such a quantum simulator has access to the regime in between the small and large polaron regimes, which cannot be described perturbatively.

Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions.

The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are examined. Particularly, it is shown that independently on the potential range, in the strong interaction limit bosonic and fermionic solutions become degenerate. For sufficiently large ranges a specific crystallization appears in the system. The results are compared to predictions of the celebrated Busch et al. model and those obtained in the Tonks-Girardeau limit. The assumed inter-particle potential is very similar to the potential between ultra-cold dressed Rydberg atoms. Therefore, the model can be examined experimentally.

On the observability of Pauli crystals in experiments with ultracold trapped Fermi gases.

The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high-order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent. These geometric structures, called Pauli crystals, are predicted for a system of N identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of the system. Here we study how fragile Pauli crystals are when realistic experimental limitations are taken into account. The influence of the number of single-shots pictures available to analysis, thermal fluctuations and finite efficiency of detection are considered. The role of these sources of noise on the possibility of experimental observation of Pauli crystals is shown and conditions necessary for the detection of the geometrical arrangements of particles are identified.

Analysis of Feedback Mechanisms with Unknown Delay Using Sparse Multivariate Autoregressive Method.

This paper discusses the study of two interacting processes in which a feedback mechanism exists between the processes. The study was motivated by problems such as the circadian oscillation of gene expression where two interacting protein transcriptions form both negative and positive feedback loops with long delays to equilibrium. Traditionally, data of this type could be examined using autoregressive analysis. However, in circadian oscillation the order of an autoregressive model cannot be determined a priori. We propose a sparse multivariate autoregressive method that incorporates mixed linear effects into regression analysis, and uses a forward-backward greedy search algorithm to select non-zero entries in the regression coefficients, the number of which is constrained not to exceed a pre-specified number. A small simulation study provides preliminary evidence of the validity of the method. Besides the circadian oscillation example, an additional example of blood pressure variations using data from an intervention study is used to illustrate the method and the interpretation of the results obtained from the sparse matrix method. These applications demonstrate how sparse representation can be used for handling high dimensional variables that feature dynamic, reciprocal relationships.

Non-standard Hubbard models in optical lattices: a review.

Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.

Results of two-stage operative treatment of anteromedial instability of the knee.

BACKGROUND: Proper treatment of massive knee injuries still constitutes a challenge for clinicians. Most often a torsion knee injury results in a rupture of the medial collateral ligament and anterior cruciate ligament. There is still no consensus on whether total rupture (Grade III) of the medial collateral ligament requires surgery, but it is well known that anterior cruciate ligament injury will require reconstructive surgery. MATERIAL AND METHODS: A total of 27 patients treated with two-staged surgery (primary MCL repair and delayed ACL reconstruction) were enrolled. Treatment outcomes were evaluated using the IKDC scale and Lysholm scale. The range of motion and knee stability was assessed during a clinical examination. Radiographs were used to evaluate the placement of suture anchors and development of osteoarthritic lesions. Static and dynamic ultrasound examinations were also performed to assess the post-operative morphology and performance of the medial collateral ligament. RESULTS: The patients who had undergone surgery for combined anteromedial instability of the knee, achieved good or very good clinical outcome according to the IKDC scale (63%, 17 of 27) and the Lysholm scale (74%, 20 of 27). Unsatisfactory functional outcomes were more often seen in older patients. Some patients developed complications, which significantly worsened the outcome. Those mainly included a limited range of movement, arthrofibrosis and Pellegrini-Stieda lesions. CONCLUSIONS: 1.Two-stage operative treatment produces good or very good results in most patients. Nevertheless, there is a risk of complications in some cases, mostly in patients aged 40 years. Accordingly, two-stage treatment is currently recommended in younger individuals. 2. A complete MCL tear at the distal attachment should be given particular attention. Although such injury is rare, due to the anatomical determinants and the risk of Stener-like lesions, i.e. unhealed ML, surgery is recommended. Surgery produces good clinical and functional results.

Tunneling-induced restoration of the degeneracy and the time-reversal symmetry breaking in optical lattices.

We study the ground-state properties of bosons loaded into the p band of a one-dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain range of tunneling strength, the full many-body ground state of the system becomes degenerate. In this region, an additional symmetry of the system, namely, the parity of the occupation number of the chosen orbital, is spontaneously broken. The state with a nonvanishing staggered angular momentum, which breaks the time-reversal symmetry, becomes the true ground state of the system.

Hyper-elastic modelling of intervertebral disc polyurethane implant.

Artificial materials including various kinds of polymers like polyurethanes are more and more widely used in different branches of science and also in biomedical engineering. The paper presents the process of creating a constitutive equation for a polyurethane nanocomposite which is considered to be hyper-elastic. The constitutive modelling was conducted within the range of application of the material as one of the components of lumbar intervertebral disc prosthesis. In the paper, the biomechanics of the lumbar spine and the most frequently applied intervertebral disc prostheses are described. Also a polyurethane nanocomposite as a new material to be applied in prostheses is presented. The way of formulating a constitutive equation by means of mathematical formulae is described. Four various hyper-elastic potential functions are considered, i.e., Ogden, Neo-Hookean, Yeoh and Mooney-Rivlin. On the basis of monotonic compression tests the best hyper-elastic model for the material considered was chosen and hyper-elastic constants were calibrated. Finally, the constitutive model was validated on the basis of FE analysis. The paper ends with a conclusion and presentation of further plans of research directed towards the development of a constitutive equation and its application in computer simulations by means of the finite element method.

Creation on demand of higher orbital states in a vibrating optical lattice.

It is shown that the extended Hubbard Hamiltonian describing atoms confined in an optical lattice always contains commonly neglected terms which can significantly change the dynamical properties of the system. Particularly for bosonic systems, they can be exploited for creating orbital states on demand via the parametric resonance phenomenon. This indicates an additional application for optical lattices, namely, the study and emulation of interactions between particles and lattice vibrations.

Dipolar molecules in optical lattices.

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.

[Characteristic of the patients' gait with recurrent lateral patella dislocation]. / Charakterystyka chodu chorych na nawracajace boczne zwichniecie rzepki.

UNLABELLED: Recurrent lateral patella dislocation, as a kind of patellofemoral malalignment, significantly influences knee biomechanics by the changing patellofemoral movement during flexion and during gait. So far other papers doesn't describe characteristic of the patients' gait with recurrent lateral patella dislocation. THE AIM OF THIS STUDY: To evaluate gait pattem patients with recurrent lateral patella luxation in comparison to normal gait pattern. MATERIAL AND METHODS: There have been 10 patients involved in evaluation. Those patients have been diagnosed recurrent lateral patella luxation. All of the patients were subjected analysis using objective system of movement analysis VICON 460. RESULTS: The results of gait parameters analysis revealed significant changes in comparison with normal pattern gait. CONCLUSIONS: Gait pattern patients with recurrent lateral patella luxation unlike normal gait pattern characterizes itself with decrease of gait speed, steps frequency reduction and hyperextension of the knee during foot of gait phase.

[Changes in gait pattern in patients with recurrent patella dislocations after tibial tuberosity transfer by modified Elmsllie-Trillat procedure]. / Zmiany stereotypu chodu chorych na nawracajace boczne zwichniecie rzepki po osteotomii guzowatosci kosci piszczelowej zmodyfikowanym sposobem Elmsllie-Trillata.

UNLABELLED: Recurrent lateral patella dislocation, as a kind of patellofemoral malalignment, significantly influences knee biomechanics by the changing patellofemoral movement during flexion and during gait. So far other papers doesn't describe characteristic of the patients' gait with recurrent lateral patella dislocation. THE AIM OF THIS STUDY: To evaluate gain pattern patients with recurrent lateral patella luxation in comparison to normal gait pattern. MATERIAL AND METHODS: There have been 6 patients involved in evaluation. Those patients have been diagnosed recurrent lateral patella luxation. All of the patients were subjected analysis using objective system of movement analysis VICON 460. RESULTS: The results of gait parameters analysis revealed significant changes in comparison with normal pattern gait. CONCLUSIONS: Gait pattern patients with recurrent lateral patella luxation unlike normal gain pattern characterizes itself with decrease of gait speed, steps frequency reduction and hyperextension of the knee during foot of gait phase.