Oscillatory dynamics in a model of vascular tumour growth -- implications for chemotherapy

Background\ud \ud Investigations of solid tumours suggest that vessel occlusion may occur when increased pressure from the tumour mass is exerted on the vessel walls. Since immature vessels are frequently found in tumours and may be particularly sensitive, such occlusion may impair tumour blood flow and have a negative impact on therapeutic outcome. In order to study the effects that occlusion may have on tumour growth patterns and therapeutic response, in this paper we develop and investigate a continuum model of vascular tumour growth.\ud Results\ud \ud By analysing a spatially uniform submodel, we identify regions of parameter space in which the combination of tumour cell proliferation and vessel occlusion give rise to sustained temporal oscillations in the tumour cell population and in the vessel density. Alternatively, if the vessels are assumed to be less prone to collapse, stable steady state solutions are observed. When spatial effects are considered, the pattern of tumour invasion depends on the dynamics of the spatially uniform submodel. If the submodel predicts a stable steady state, then steady travelling waves are observed in the full model, and the system evolves to the same stable steady state behind the invading front. When the submodel yields oscillatory behaviour, the full model produces periodic travelling waves. The stability of the waves (which can be predicted by approximating the system as one of λ-ω type) dictates whether the waves develop into regular or irregular spatio-temporal oscillations. Simulations of chemotherapy reveal that treatment outcome depends crucially on the underlying tumour growth dynamics. In particular, if the dynamics are oscillatory, then therapeutic efficacy is difficult to assess since the fluctuations in the size of the tumour cell population are enhanced, compared to untreated controls.\ud Conclusions\ud \ud We have developed a mathematical model of vascular tumour growth formulated as a system of partial differential equations (PDEs). Employing a combination of numerical and analytical techniques, we demonstrate how the spatio-temporal dynamics of the untreated tumour may influence its response to chemotherapy.\ud Reviewers\ud \ud This manuscript was reviewed by Professor Zvia Agur and Professor Marek Kimmel

A subradiant optical mirror formed by a single structured atomic layer

Efficient and versatile interfaces for the interaction of light with matter are an essential cornerstone for quantum science. A fundamentally new avenue of controlling light-matter interactions has been recently proposed based on the rich interplay of photon-mediated dipole-dipole interactions in structured subwavelength arrays of quantum emitters. Here we report on the direct observation of the cooperative subradiant response of a two-dimensional (2d) square array of atoms in an optical lattice. We observe a spectral narrowing of the collective atomic response well below the quantum-limited decay of individual atoms into free space. Through spatially resolved spectroscopic measurements, we show that the array acts as an efficient mirror formed by only a single monolayer of a few hundred atoms. By tuning the atom density in the array and by changing the ordering of the particles, we are able to control the cooperative response of the array and elucidate the interplay of spatial order and dipolar interactions for the collective properties of the ensemble. Bloch oscillations of the atoms out of the array enable us to dynamically control the reflectivity of the atomic mirror. Our work demonstrates efficient optical metamaterial engineering based on structured ensembles of atoms and paves the way towards the controlled many-body physics with light and novel light-matter interfaces at the single quantum level.Comment: 8 pages, 5 figures + 12 pages Supplementary Infomatio

Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.Comment: 4 pages, 1 figur

Quantum tunneling across spin domains in a Bose-Einstein condensate

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure in the boundary between spin domains which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1 spinor Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure

Suppression and enhancement of impurity scattering in a Bose-Einstein condensate

Impurity atoms propagating at variable velocities through a trapped Bose-Einstein condensate were produced using a stimulated Raman transition. The redistribution of momentum by collisions between the impurity atoms and the stationary condensate was observed in a time-of-flight analysis. The collisional cross section was dramatically reduced when the velocity of the impurities was reduced below the speed of sound of the condensate, in agreement with the Landau criterion for superfluidity. For large numbers of impurity atoms, we observed an enhancement of atomic collisions due to bosonic stimulation. This enhancement is analogous to optical superradiance.Comment: 4 pages, 4 figure

Spin correlation and Discrete symmetry in Spinor Bose-Einstein Condensates

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal 2 channel. We show the low energy spin dynamics in the system can be mapped into an $o(n)$ nonlinear sigma model(NL$\sigma$M). $n=3$ at the zero magnetic field limit and $n=2$ in the presence of weak magnetic fields. In an ordered phase, the ground state has a hidden $Z_2$ symmetry and is degenerate under the group $[U(1)\times S^{n-1}]/Z_2$. We explore consequences of the hidden symmetry and propose some measurements to probe it.Comment: 4 pages; published version in Phys. Rev. Lett. vol 87, 080401-1(2001

Ground state energy of the f=1f=1 spinor Bose-Einstein condensates

We calculate, in the standard Bogoliubov approximation, the ground state energy of the spinor BEC with hyperfine spin $f=1$ where the two-body repulsive hard-core and spin exchange interactions are both included. The coupling constants characterized these two competing interactions are expressed in terms of the corresponding s-wave scattering lengths using second-order perturbation methods. We show that the ultraviolet divergence arising in the ground state energy corrections can be exactly eliminated.Comment: 14 pages, no figures, submitted to PR

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate

A central goal in condensed matter and modern atomic physics is the exploration of many-body quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensed-matter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor Bose-Einstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. $^{87}$Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Comment: 6 pages, 4 figure

Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate

We propose an experiment that would demonstrate nonlinear Josephson-type oscillations in the relative population of a driven, two-component Bose-Einstein condensate. An initial state is prepared in which two condensates exist in a magnetic trap, each in a different hyperfine state, where the initial populations and relative phase between condensates can be controlled within experimental uncertainty. A weak driving field is then applied, which couples the two internal states of the atom and consequently transfers atoms back and forth between condensates. We present a model of this system and investigate the effect of the mean field on the dynamical evolution.Comment: 4 pages, 3 fig

Excitation-assisted inelastic processes in trapped Bose-Einstein condensates

We find that inelastic collisional processes in Bose-Einstein condensates induce local variations of the mean-field interparticle interaction and are accompanied by the creation/annihilation of elementary excitation. The physical picture is demonstrated for the case of three body recombination in a trapped condensate. For a high trap barrier the production of high energy trapped single particle excitations results in a strong increase of the loss rate of atoms from the condensate.Comment: 4 pages, no figure