Grassmann phase space theory for fermions

A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases

Glauber-Sudarshan P-representations for fermions

The Glauber-Sudarshan P-representation is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart. We present a derivation of both the bosonic and fermionic distributions and, in doing so, demonstrate the reason for the existence of two distinct fermionic forms and the relationship between these. We consider both single mode systems and also multiparticle systems with many modes. For simplicity only one type of boson or fermion will be considered.Comment: To appear in Physica Scripta (2023

Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory

Discrete time crystals (DTCs) refer to a novel many-body steady state that spontaneously breaks the discrete time-translational symmetry in a periodically-driven quantum system. Here, we study DTCs in a Bose-Einstein condensate (BEC) bouncing resonantly on an oscillating mirror, using a two-mode model derived from a standard quantum field theory. We investigate the validity of this model and apply it to study the long-time behavior of our system. A wide variety of initial states based on two Wannier modes are considered. We find that in previous studies the investigated phenomena in the evolution time-window ($\lessapprox$2000 driving periods) are actually "short-time" transient behavior though DTC formation signaled by the sub-harmonic responses is still shown if the inter-boson interaction is strong enough. After a much longer (about 20 times) evolution time, initial states with no "long-range" correlations relax to a steady state, where time-symmetry breaking can be unambiguously defined. Quantum revivals also eventually occur. This long-time behavior can be understood via the many-body Floquet quasi-eigenenergy spectrum of the two-mode model. A symmetry-breaking edge for DTC formation appears in the spectrum for strong enough interaction, where all quasi-eigenstates below the edge are symmetry-breaking while those above the edge are symmetric. The late-time steady state's time-translational symmetry depends solely on whether the initial energy is above or below the symmetry-breaking edge. A phase diagram showing regions of symmetry-broken and symmetric phases for differing initial energies and interaction strengths is presented. We find that according to this two-mode model, the discrete time crystal survives for times out to at least 250,000 driving periods

Discrete Time Crystals with Absolute Stability

We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of discrete time crystal states to low-lying eigenstates of a time-independent model that reveals spontaneous breaking of space translation symmetry. The mapping ensures that there are no residual time-dependent terms that could lead to heating of the system and destruction of discrete time crystals. We also analyze periodically kicked bosons where the mapping is approximate only and cannot guarantee the absolute stability of discrete time crystals. Besides illustrating potential sources of instability, the kicked bosons model demonstrates a rich field for investigating the interplay between different time and space symmetry breaking, as well as the stability of time crystal behavior in contact with a thermal reservoir.Comment: Version accepted for publication in Physical Review B as a Lette

Glauber P-representations for fermions

The Glauber-Sudarshan P-representation for bosons is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart, introduced by Cahill and Glauber. We present a derivation of both the bosonic and fermionic distributions and, in doing so, demonstrate the reason for the existence of two distinct fermionic forms and the relationship between these. We consider both single mode systems and also multiparticle systems with many modes. Expressions for the moments involving products of mode annihilation and creation operators are obtained. For simplicity only one type of boson or fermion will be considered, but generalising to more types is straightforward

Eccentricity Evolution in Simulated Galaxy Clusters

Strong cluster eccentricity evolution for $z \le 0.13$ has appeared in a variety of observational data sets. We examine the evolution of eccentricity in simulated galaxy clusters using a variety of simulation methodologies, amplitude normalizations, and background cosmologies. We do not find find such evolution for $z < 0.1$ in any of our simulation ensembles. We suggest a systematic error in the form of a redshift-dependent selection effect in cluster catalogs or missing physics in cluster simulations important enough to modify the cluster morphology.Comment: Revised version to be published in ApJ. Moderate revisions, including additional N-body simulations with varying amplitude normalization and background matter density within OCDM and $\lambda$CDM scenarios reinforce our conclusion that observed clusters have recently relaxed much more rapidly than simulated one

Engineering a hyperactive TcBuster transposase for efficient gene delivery for cell therapy applications

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