Finite-size effects in the dynamics of few bosons in a ring potential

We study the temporal evolution of a small number $N$ of ultra-cold bosonic atoms confined in a ring potential. Assuming that initially the system is in a solitary-wave solution of the corresponding mean-field problem, we identify significant differences in the time evolution of the density distribution of the atoms when it instead is evaluated with the many-body Schr\"odinger equation. Three characteristic timescales are derived: the first is the period of rotation of the wave around the ring, the second is associated with a "decay" of the density variation, and the third is associated with periodic "collapses" and "revivals" of the density variations, with a factor of $\sqrt N$ separating each of them. The last two timescales tend to infinity in the appropriate limit of large $N$, in agreement with the mean-field approximation. These findings are based on the assumption of the initial state being a mean-field state. We confirm this behavior by comparison to the exact solutions for a few-body system stirred by an external potential. We find that the exact solutions of the driven system exhibit similar dynamical features.Comment: To appear in Journal of Physics

Phase diagram of a rapidly-rotating two-component Bose gas

We derive analytically the phase diagram of a two-component Bose gas confined in an anharmonic potential, which becomes exact and universal in the limit of weak interactions and small anharmonicity of the trapping potential. The transitions between the different phases, which consist of vortex states of single and multiple quantization, are all continuous because of the addition of the second component.Comment: 5 pages, 3 figure

Direct simulation for a homogenous gas

A probabilistic analysis of the direct simulation of a homogeneous gas is given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced probability densities is derived. By invoking the molecular chaos assumption, an equation similar to the Boltzmann equation for the single particle probability density and the corresponding H-theorem is derived

Rotational properties of non-dipolar and dipolar Bose-Einstein condensates confined in annular potentials

We investigate the rotational response of both non-dipolar and dipolar Bose-Einstein condensates confined in an annular potential. For the non-dipolar case we identify certain critical rotational frequencies associated with the formation of vortices. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms.Comment: 5 pages, 4 figure

Spin-orbit-coupled Bose-Einstein-condensed atoms confined in annular potentials

A spin-orbit-coupled Bose-Einstein-condensed cloud of atoms confined in an annular trapping potential shows a variety of phases that we investigate in the present study. Starting with the non-interacting problem, the homogeneous phase that is present in an untrapped system is replaced by a sinusoidal density variation in the limit of a very narrow annulus. In the case of an untrapped system there is another phase with a striped-like density distribution, and its counterpart is also found in the limit of a very narrow annulus. As the width of the annulus increases, this picture persists qualitatively. Depending on the relative strength between the inter- and the intra-components, interactions either favor the striped phase, or suppress it, in which case either a homogeneous, or a sinusoidal-like phase appears. Interactions also give rise to novel solutions with a nonzero circulation.Comment: Final, slightly revised versio

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.Comment: 8 pages, 5 figure

Differences in Neuromuscular Adaptations After Two Weeks of Conventional vs Blood Flow Restriction Resistance Training

PURPOSE: The purpose of the study was to determine the neuromuscular changes in the rectus femoris (RF) muscle as measured by electromyography (EMG) following short-term resistance training with and without blood flow restriction (BFR). METHODS: 12 males (age = 27.4 ± 6.3 years; height = 171 ± 7 cm; weight = 79.8 ± 13.2 kg) performed six sessions of lower body unilateral resistance training using a leg extension machine. The leg on which BFR was applied was determined through randomization leg dominance Each training session consisted of unilateral knee extensions with and without blood flow restriction. Electromyography data was recorded for each participant during two isometric maximum voluntary contractions (MVC) and two isokinetic knee extension tests (180°/s and 60°/s) using a Biodex System 4 Pro™. EMG was recorded from the RF during these tests. Resistance training consisted of six non-consecutive sessions of knee extension exercises performed in a time frame of two weeks. For the BFR group, subjects trained for a total of four sets (30, 15, 15, 15) at an intensity of 20% 1RM. The contralateral limb was trained with two sets of 11 repetitions at an intensity of 70% 1RM without BFR. The volume of exercises was similar for both conditions. RESULTS: No condition*time interactions or condition and time main effects were observed for root mean square (RMS), mean RMS, yMax, and median frequency (MDF) in both MVC and isokinetic 180°/s and 60°/s (p\u3e0.05). CONCLUSIONS: Both training conditions resulted in insignificant changes and there was no significant difference found between time points. It could be concluded that this was not enough time or stimulus to note major differences across modalities in relation to neuromuscular adaptations of the RF as measured by EMG. Further studies should investigate the effects of higher volume load on neuromuscular adaptations

The Evolution of Blood Flow Restricted Exercise

The use of blood flow restricted (BFR) exercise has become an accepted alternative approach to improve skeletal muscle mass and function and improve cardiovascular function in individuals that are not able to or do not wish to use traditional exercise protocols that rely on heavy loads and high training volumes. BFR exercise involves the reduction of blood flow to working skeletal muscle by applying a flexible cuff to the most proximal portions of a person\u27s arms or legs that results in decreased arterial flow to the exercising muscle and occluded venous return back to the central circulation. Safety concerns, especially related to the cardiovascular system, have not been consistently reported with a few exceptions; however, most researchers agree that BFR exercise can be a relatively safe technique for most people that are free from serious cardiovascular disease, as well as those with coronary artery disease, and also for people suffering from chronic conditions, such as multiple sclerosis, Parkinson\u27s, and osteoarthritis. Potential mechanisms to explain the benefits of BFR exercise are still mostly speculative and may require more invasive studies or the use of animal models to fully explore mechanisms of adaptation. The setting of absolute resistive pressures has evolved, from being based on an individual\u27s systolic blood pressure to a relative measure that is based on various percentages of the pressures needed to totally occlude blood flow in the exercising limb. However, since several other issues remain unresolved, such as the actual external loads used in combination with BFR, the type of cuff used to induce the blood flow restriction, and whether the restriction is continuous or intermittent, this paper will attempt to address these additional concerns

Comparison of Skeletal Muscle Tissue Oxygen Saturation Responses between Genders

Special attention should be given to subcutaneous thigh fat accrual and its impact on the amount of skeletal muscle blood flow and accumulation when using different initial restrictive pressure (IRP) during blood flow restriction (BFR) training. Due to different patterns of fat distribution and deposition in males and females, it is important to test the effects of subcutaneous fat on tissue oxygenation and lactate production during exercises with BFR. PURPOSE: The present study investigated the importance of thigh subcutaneous fat as a variable that may be associated with affecting the magnitude of initial pressure (tightness of cuffs before inflation with air) on skeletal muscle tissue oxygen saturation and lactate between males and females. METHODS: Twenty healthy volunteers, 10 males (25 ± 4.83 yr) and 10 females (20.7 ± 1.06 yr), performed exercises with an IRP of 40mmHg. The following procedures were performed in order: a) subcutaneous fat thickness, b) pre-maximal isometric force (MVC), c) 4 sets (1 × 30 reps and 3 × 15 reps) of dynamic knee extension exercises performed at 20% MVC, d) post-MVC. Skeletal muscle tissue oxygen saturation was continuously monitored before, during, and after exercises with near-infrared spectroscopy placed to a mark that was made at 50% on the line from the anterior superior iliac spine to the superior part of the patella. Plasma lactate levels were assessed prior to, in between the first and second set, immediately after post MVC, 5min-post, 10 min-post, and 20 min-post. RESULTS: Thigh subcutaneous fat thickness was significantly greater in females than males (p\u3c0.01). Tissue oxygenation significantly decreased (p\u3c0.03) throughout exercise in both genders with an observed significant time × gender interaction (p\u3c0.01). Both male and females responded to the BFR similarly with a significant decrease (p\u3c0.01) in peak force production from pre to post exercise, while plasma lactate levels significantly differed (p\u3c0.01) throughout the exercise with no time × gender interaction (p\u3c0.3). CONCLUSION: The observed gender difference in tissue oxygenation in response to BFR with an IRP of 40mmHg underline the necessity for future studies to consider subcutaneous fat as a variable to influence the magnitude of physiological adaptations between genders and adjust the IRP accordingly

Neuromuscular Responses during Knee Extension Exercise in Combination with Different Blood Flow Restriction Initial Pressures

Specifications of blood flow restriction training technique have been widely discussed to create a valid and reliable protocol. One of the unexplored variables is the effect of different initial restrictive pressures (tightness of cuffs, IRP) in combination with resistance exercise on neuromuscular responses and strength. PURPOSE: The purpose of this study was to determine any differences in amplitude (RMS) and median frequency (MDF) of electromyography (EMG) signals, as well as changes in strength during knee extension exercises with IRPs of 40-45 mmHg and 60-65 mmHg. METHODS: Twenty male subjects (age = 25.7 ± 4.3 yrs), participated in this study. They were required to attend the lab on 3 different occasions, with the first one being a familiarization session. On the subsequent sessions, participant\u27s upper leg was measured starting from the lateral epicondyle to the greater trochanter of the femur. An EMG electrode was placed at one-third the distance over the longitudinal axis of the vastus lateralis (VL) after shaving, abrading and cleaning with isopropyl alcohol. Initial restrictive pressure was randomly selected and participants completed a pre-exercise maximum voluntary contraction (MVC) test to determine their torque. For dynamic exercises, load was set at 20% MVC and each participant performed one set of 30 repetitions and three sets of 15 repetitions, separated by one minute rest. Post-exercise MVC was performed to assess the changes in leg strength following exercises. RESULTS: Results showed significant main effects (p\u3c0.01) in leg strength for condition (40-45 mmHg vs. 60-65 mmHg) and trial (pre vs. post MVC). A significant main effect was observed for condition for MVC EMG amplitude (p\u3c0.01). In addition, there were significant main effects for contractions (p\u3c0.01) in both EMG amplitude and MDF during dynamic exercises. CONCLUSION: The significant decreases in knee extension strength at IRP of 60-65 mmHg compared to IRP of 40-45mmHg from pre- to post-exercise suggest that subjects experienced more fatigue at 60-65 mmHg because of the decreased availability of oxygen to the working muscle. The use of different IRP will affect the level of blood flow and oxygen supply to skeletal muscle possibly causing variation in neuromuscular adaptation due to changes in total and type of muscle fiber recruitment