Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems-the sawtooth lattice-filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.
By constructing a hydrodynamic canonical formalism, we show that the occurrence of an arbitrary density-dependent gauge potential in the meanfield Hamiltonian of a Bose-condensed fluid invariably leads to nonlinear flow-dependent terms in the wave equation for the phase, where such terms arise due to the explicit dependence of the mechanical flow on the fluid density. In addition, we derive a canonical momentum transport equation for this class of nonlinear fluid and obtain an expression for the stress tensor. Further, we study the hydrodynamic equations in a particular nonlinear fluid, where the effective gauge potential results from the introduction of weak contact interactions in an ultracold dilute Bose gas of optically-addressed two-level atoms. In the Cauchy equation of mechanical momentum transport of the superfluid, two non-trivial terms emerge due to the density-dependent vector potential. A body-force of dilation appears as a product of the gauge potential and the dilation rate of the fluid, while the stress tensor features a canonical flow pressure term given by the inner-product of the gauge potential and the canonical current density. By numerical simulation, we illustrate an interesting effect of the nonlinear gauge potential on the groundstate wavefunction of a superfluid in the presence of a foreign impurity. We find that the groundstate adopts a non-trivial local phase, which is antisymmetric under reversal of the gauge potential. The phase profile leads to a canonical-flow or phase-flow dipole about the impurity, resulting in a skirting mechanical flow. As a result, the pressure becomes asymmetric about the object and the condensate undergoes a deformation.
We consider interacting one-dimensional, spinless Fermi gases, whose lowenergy properties are described by Luttinger liquid theory. We perform a systematic, in-depth analysis of the relation between the macroscopic, phenomenological parameters of Luttinger liquid effective field theory, and the microscopic interactions of the Fermi gas. In particular, we begin by explaining how to model effective interactions in one dimension, which we then apply to the main forward scattering channel -the interbranch collisionscommon to these systems. We renormalise the corresponding interbranch phenomenological constants in favour of scattering phase shifts. Interestingly, our renormalisation procedure shows (i) how Luttinger's model arises in a completely natural way -and not as a convenient approximation -from Tomonaga's model, and (ii) the reasons behind the interbranch coupling constant remaining unrenormalised in Luttinger's model. We then consider the so-called intrabranch processes, whose phenomenological coupling constant
We present a novel combination of generative and predictive machine learning models for discovering unique protein inhibitors. The new method is assessed on its ability to generate unique inhibitors for the cancer associated protein kinase, CDK9. We validate our method by performing biochemical assays, attaining a hit rate of more than 10%, demonstrating the method to be a notable improvement upon a more standard, and somewhat naive approach. Moreover, we imposed the additional challenge of finding inhibitors that are readily synthesized. Importantly, two new inhibitors are found, with one being distinct from reported CDK9 inhibitors. We discuss the results in the context of modern machine learning principles and the desire expressed by the rational drug design community to secure molecules that are structurally different, yet with high binding affinities, to structurally determined protein targets.
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