In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological b
ackgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous studies done for a scalar field. We characterize the quantizations fulfilling the criteria above and we show that they form a unique equivalence class of unitarily related quantizations, which provide a well-defined number of created particles at all finite times.
Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools, we approach
this problem in order to describe the transition between two such synchronized states. Bifurcation and continuation analysis provide a full description of the parameter space. Phase approximation modeling allows the calculation of the oscillator periods and the bifurcation point.
We introduce the package GraphicalModelsMLE for computing the maximum likelihood estimator (MLE) of a Gaussian graphical model in the computer algebra system Macaulay2. The package allows to compute for the class of loopless mixed graphs. Additional
functionality allows to explore the underlying algebraic structure of the model, such as its ML degree and the ideal of score equations.
Incorporating multifunctionality along with the spin-related phenomenon in a single device is of great interest for the development of next generation spintronic devices. One of these challenges is to couple the photo-response of the device together
with its magneto-response to exploit the multifunctional operation at room temperature. Here, the multifunctional operation of a single layer p-type molecular spin valve is presented, where the device shows a photovoltaic effect at the room temperature on a transparent glass substrate. The generated photovoltage is almost three times larger than the applied bias to the device which facilitates the modulation of the magnetic response of the device both with bias and light. It is observed that the photovoltage modulation with light and magnetic field is linear with the light intensity. The device shows an increase in power conversion efficiency under magnetic field, an ability to invert the current with magnetic field and under certain conditions it can act as a spin-photodetector with zero power consumption in the standby mode. The room temperature exploitation of the interplay among light, bias and magnetic field in the single device with a p-type molecule opens a way towards more complex and efficient operation of a complete spin-photovoltaic cell.
It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. left vs. right) and become increasingly polarized. We provide an agent-based model that reproduces these two stylized facts as emerg
ent properties of an opinion dynamics in a multi-dimensional space of continuous opinions. The mechanisms for the change of agents opinions in this multi-dimensional space are derived from cognitive dissonance theory and structural balance theory. We test assumptions from proximity voting and from directional voting regarding their ability to reproduce the expected emerging properties. We further study how the emotional involvement of agents, i.e. their individual resistance to change opinions, impacts the dynamics. We identify two regimes for the global and the individual alignment of opinions. If the affective involvement is high and shows a large variance across agents, this fosters the emergence of a dominant ideological dimension. Agents align their opinions along this dimension in opposite directions, i.e. create a state of polarization.
The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted. Its sandpil
e group is the direct sum of cyclic groups of orders given by quotients of greatest common divisors of minors of its Laplacian matrix. We show these greatest common divisors can be expressed in terms of monomials in the graphs edge multiplicities.
The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Qsubseteq V$ of query ve
rtices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $mathbf{P} = mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).
Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network m
odels based on experimental data and biological input. The key feature is a discrete analog of parameter estimation for continuous models. With only experimental data as input, the software can be used as a tool for reverse-engineering of Boolean network models from experimental time course data.
