Search Results (3)

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins $\overrightarrow{\mu }$ is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as $F_{magn}^{en}~\frac{1}{r^3}$, where r is the distance between the edge of the string and the current I, and $k_B$ is the Boltzmann constant; ($r\gg L$ is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as $F_{magn}^{en}~\frac{1}{T}$, which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed. Full article

We consider a quantum spinless nonrelativistic charged particle moving in the $xy$ plane under the action of a time-dependent magnetic field, described by means of the linear vector potential $\mathbf{A}=B(t)\left[-y(1+\alpha ),x(1-\alpha )\right]/2$, with two fixed values of the gauge parameter $\alpha$: $\alpha =0$ (the circular gauge) and $\alpha =1$ (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for $\alpha =0$ and straight lines for $\alpha =1$. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function $B(t)$. They are expressed in terms of solutions to the classical equation of motion $\ddot{\epsilon }+{\omega }_{\alpha }^2(t)\epsilon =0$, with ${\omega }_1=2{\omega }_0$. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions $B(t)$, when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value. Full article

Simulating the evolution of quantum systems on a classical computer is a yellow very challenging task, which could be easily tackled by digital quantum simulators. These are intrinsically quantum devices whose parameters can be controlled in order to mimic the evolution of a broad class of target Hamiltonians. We describe here a quantum simulator implemented on a linear register of molecular Cr₇Ni qubits, linked through Co²⁺ ions which act as switches of the qubit–qubit interaction. This allows us to implement one- and two-qubit gates on the chain with high-fidelity, by means of uniform magnetic pulses. We demonstrate the effectiveness of the scheme by numerical experiments in which we combine several of these elementary gates to implement the simulation of the transverse field Ising model on a set of three qubits. The very good agreement with the expected evolution suggests that the proposed architecture can be scaled to several qubits. Full article