Related papers: Nondifferentiable Dynamic: Two Examples
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values…
The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic…
We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice…
The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the…
We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the…
We analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations iff the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
The quantum theory of a free particle on a portion of two-dimensional Euclidean space bounded by a circle and subject to non-local boundary conditions gives rise to bulk and surface states. Starting from this well known property, a…
When two or more objects move relative to one another in vacuum, they experience a drag force which, at zero temperature, usually goes under the name of quantum friction. This contactless non-conservative interaction is mediated by the…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
Gravitons in a squeezed vacuum state, the natural result of quantum creation in the early universe or by black holes, will introduce metric fluctuations. These metric fluctuations will introduce fluctuations of the lightcone. It is shown…
The path integral of 4D Einstein-Hilbert gravity for the de Sitter-like Universe with fluctuations is investigated, and the transition amplitude from one boundary configuration to another is computed. The gravitational system is described…
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $\beta$-functions for all…
In Verlinde's theory of entropic gravity, the internal degrees of freedom are marked by "bits", but the microscopic origin of "bits" is unknown hitherto. To this direction, we adopt the quantum harmonic oscillators to naively model the…
The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…
Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first order…