We consider the system of the Rosenzweig-MacArthur equations with one consumer and two resources. Recently, the model has been generalized by including an optimization of the consumption rates βi [P. Gawroński et a...
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We consider the system of the Rosenzweig-MacArthur equations with one consumer and two resources. Recently, the model has been generalized by including an optimization of the consumption rates βi [P. Gawroński et al., Chaos 32, 093121 (2022)]. Also, we have assumed that β1+β2=1, which reflects the limited amount of time that can be devoted to a given type of resource. Here we investigate the transition to the phase where one of the resources becomes extinct. The goal is to show that the stability of the phase with two resources strongly depends on the initial value of βi. Our second goal is to demonstrate signatures of transient chaos in the time evolution.
Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement mod...
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Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the puzzle of information disturbance. Two distinct questions are then in order. First, what is the minimum disturbance a measurement may induce? Second, when a fixed disturbance occurs, how informative is the possible measurement in the best-case scenario? Here we propose various approaches to tackle these questions and provide explicit solutions for the set of unbiased binary qubit measurements and postmeasurement state spaces that are equivalent to the image of a unital qubit channel. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces as well as the sharpness and quantum resources preserved in the postmeasurement states in terms of coherence and discordlike correlation once the measurement is applied locally.
We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous, and global update rule. The dyn...
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We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous, and global update rule. The dynamics has a very rich spectrum of attractors including fixed points and limit cycles, the length and number of which change with the size of the system. In this paper we concentrate on a class of limit cycles that preserve energy spectrum of the consecutive states. We call such limit cycles perfect. Consecutive states in a perfect cycle are separated from each other by the same Hamming distance. Also the Hamming distance between any two states separated by k steps in a perfect cycle is the same for all such pairs of states. The states of a perfect cycle form a very symmetric trajectory in the configuration space. We argue that the symmetry of the trajectories is rooted in the permutation symmetry of vertices of the network and a local symmetry of a certain energy function measuring the level of balance and frustration of triads.
We consider a neutral exciton localized on a model p−i−n junction defined in a two-dimensional crystal, MoSe2 and phosphorene, using a variational approach to the effective mass Hamiltonian. The variational solution t...
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We consider a neutral exciton localized on a model p−i−n junction defined in a two-dimensional crystal, MoSe2 and phosphorene, using a variational approach to the effective mass Hamiltonian. The variational solution to the problem with nonseparable center of mass provides the exciton density in the real space and accounts for the kinetic energy due to the exciton localization. For low values of the potential step across the junction, the exciton occupies an area which is much larger than the nominal width of the junction. Localization of the exciton within the junction area is accompanied by the appearance of the dipole moment induced by the local electric field. The induced dipole moment becomes a linear function of the potential step only when the step is sufficiently large. In consequence, the energy dependence on the step value is nonparabolic. We demonstrate that the exciton gets localized not exactly at the center of the junction but on the side which is more energetically favorable for the heavier carrier: electron or hole.
We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quen...
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We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quenches ground-state oscillations for a circular ring because of interrupted persistent current circulation around the ring. An elliptic deformation of the confinement potential can compensate for the anisotropy of the effective masses and produce ground-state parity transformations with the AB periodicity. Moreover, a specific ratio of the semiaxes is determined for which the spectrum becomes identical to that of a circular quantum ring and an isotropic effective mass. We identify a generalized angular momentum operator which commutes with the continuum Hamiltonian for the chosen ratio of the semiaxes that closes the avoided crossings of energy levels for states of the same parity and spin. Ground-state oscillations for the two-electron ground state are also discussed.
The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a ra...
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Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on the intercontinental level. In this paper, we address this issue by creat...
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The phenomenon of percolation is one of the core topics in statistical mechanics. It allows one to study the phase transition known in real physical systems only in a purely geometrical way. In this paper, we determin...
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The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modelin...
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The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modeling the social noise level. For that purpose, two main types of lattices are considered. The first is created by removing some links from a regular triangular lattice to produce a diluted triangular lattice, and the second by adding more links to create an enhanced triangular lattice. In both those cases, the full range of possible graph densities is discussed, limited by the extreme cases of networks which consist of a small number of separated triads and fully connected networks. It is shown that the existence of the balanced state is not possible if the average node degree is too close to the value characterizing the regular triangular lattice. Otherwise, both balanced (or partially balanced) and imbalanced states are possible, depending on the temperature. However, only for graphs which are dense enough a phase transition of the first kind is observed, while less enhanced networks (and all diluted) indicate a smooth crossover between the two states. The crossover temperatures are size independent only for the diluted triangular lattices and depend on the size of the system for the enhanced triangular lattices, as is the case also for the critical temperatures of the phase transition observed in denser enhanced lattices.
The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of fre...
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The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models featuring very good agreement with the original field-theoretic partial differential equation are constructed, including in the nonperturbative region and for relativistic velocities. The numerical solutions of the sG model describing the evolution of the kink in the presence of a barrier as well as in the case of a periodic heterogeneity under the potential additional influence of a switched bias current and/or dissipation were obtained. The results of the field equation and the effective models were favorably compared. The effect of the choice of initial conditions in the field model on the agreement of the results with the effective model is also discussed.
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