Related papers: Quantum Instabilities of Solitons
We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single…
We investigate the conditions for the emergence of wave instabilities in a vacuum cavity delimited by cylindrical metallic walls under rotation. It is shown that for a small vacuum gap and for an angular velocity exceeding a certain…
We study quantum dynamics of bosonic atoms that are excited to form a phase kink, or several kinks, by an imprinting potential in a one-dimensional trap. We calculate dissipation due to quantum and thermal fluctuations in soliton…
Numerical studies together with asymptotic and spectral analysis establish regimes where soliton pairs in degenerate optical parametric oscillators fuse, repel, or form bound states. A novel bound state stabilized by coupled internal…
There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot…
In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are…
Equations for contour dynamics of dark solitons are obtained for the general form of the nonlinearity function. Their self-similar solution which describes the nonlinear stage of the bending instability of dark solitons is studied in…
We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced…
The effect of an externally applied force upon dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a linear potential term. The potential…
The macroscopic zero-temperature behavior of weakly- incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interface-like solutions: (i)…
We study numerically the dynamics of quantized vortices and solitons induced by an oscillating potential inside a trapped Bose-Einstein condensate. The dynamics of the topological defects is much different from the case for a linear uniform…
Optical solitons are known to be classically stable objects which are robust to perturbations. In this work, we show that due to quantum mechanical effects, an optical soliton that is initially in a classical soliton coherent state will…
We revisit the phenomenon of instability of solitons in the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t + \partial_{x_1} (\Delta u + u^p) = 0, (x_1,x_2) \in…
In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…
Quantum chromodynamics in two spacetime dimensions admits a finite non-invertible symmetry described mathematically by a fusion category. This symmetry is spontaneously broken at long distances, leading to distinct vacua. When the theory…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
In this note we investigate the stability of the classical ground state of the Quantum Hall Soliton proposed recently in hep-th/0010105 . We explore two possible perturbations which are not spherically symmetric and we find that the…
Relative order \alpha(Z\alpha)^3 shift of the energy levels induced by the vacuum polarization is reexamined for a bound system of two particles with masses m and M. Recent results for hydrogen and for positronium are shown to contain an…
Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…
A set of integral relations for rotational and translational zero modes in the vicinity of the classical soliton solution are derived from the particle-like properties of the latter. The validity of these all relations is considered for a…