اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNon-adiabatic Non-cyclic Generalization of the Berry Phase for a Spin-1/2 Particle in a Rotating Magnetic Field
175
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we define a non-dynamical phase for a spin-1/2 particle in a rotating magnetic field in the non-adiabatic non-cyclic case, and this phase can be considered as a generalized Berry phase. We show that this phase reduces to the geometric Berry phase, in the adiabatic limit, up to a factor independent of the parameters of the system. We could add an arbitrary phase to the eigenstates of the Hamiltonian due to the gauge freedom. Then, we fix this arbitrary phase by comparing our Berry phase in the adiabatic limit with the Berrys result for the same system. Also, in the extreme non-adiabatic limit our Berry phase vanishes, modulo $2pi$, as expected. Although, our Berry phase is in general complex, it becomes real in the expected cases: the adiabatic limit, the extreme non-adiabatic limit, and the points at which the state of the system returns to its initial form, up to a phase factor. Therefore, this phase can be considered as a generalization of the Berry phase. Moreover, we investigate the relation between the value of the generalized Berry phase, the period of the states and the period of the Hamiltonian.
قيم البحث
اقرأ أيضاً
In this study, we considered a moving particle with a magnetic quadrupole moment in an elastic medium in the presence of a screw dislocation. We assumed a radial electric field in a rotating frame that leads a uniform effective magnetic field perpend
icular to the plane of motion. We solved the Schrodinger equation to derive wave and energy eigenvalue functions by employing analytical methods for two interaction configurations: in the absence of potential and in the presence of a static scalar potential. Due to the topological defect in the medium, we observed a shift in the angular momentum quantum number which affects the energy eigenvalues and the wave function of the system.
By using the infinite time-evolving block decimation, we study quantum fidelity and entanglement entropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field. The effects of the magnetic field on the fidelity are investigated
, and its relation with the quantum phase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge c = 1 is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.
The generalization of the geometric phase to the realm of mixed states is known as Uhlmann phase. Recently, applications of this concept to the field of topological insulators have been made and an experimental observation of a characteristic critica
l temperature at which the topological Uhlmann phase disappears has also been reported. Surprisingly, to our knowledge, the Uhlmann phase of such a paradigmatic system as the spin-$j$ particle in presence of a slowly rotating magnetic field has not been reported to date. Here we study the case of such a system in a thermal ensemble. We find that the Uhlmann phase is given by the argument of a complex valued second kind Chebyshev polynomial of order $2j$. Correspondingly, the Uhlmann phase displays $2j$ singularities, occurying at the roots of such polynomials which define critical temperatures at which the system undergoes topological order transitions. Appealing to the argument principle of complex analysis each topological order is characterized by a winding number, which happen to be $2j$ for the ground state and decrease by unity each time increasing temperature passes through a critical value. We hope this study encourages experimental verification of this phenomenon of thermal control of topological properties, as has already been done for the spin-$1/2$ particle.
We solve the Schrodinger equation for a charged particle in the non-uniform magnetic field by using the Nikiforov-Uvarov method. We find the energy spectrum and the wave function, and present an explicit relation for the partition function. We give a
nalytical expressions for the thermodynamic properties such as mean energy and magnetic susceptibility, and analyze the entropy, free energy and specific heat of this system numerically. It is concluded that the specific heat and magnetic susceptibility increase with external magnetic field strength and different values of the non-uniformity parameter, $alpha$, in the low temperature region, while the mentioned quantities are decreased in high temperature regions due to increasing the occupied levels at these regions. The non-uniformity parameter has the same effect with a constant value of the magnetic field on the behavior of thermodynamic properties. On the other hand, the results show that transition from positive to negative magnetic susceptibility depends on the values of non-uniformity parameter in the constant external magnetic field.
The geometric phase has been proposed as a candidate for noise resilient coherent manipulation of fragile quantum systems. Since it is determined only by the path of the quantum state, the presence of noise fluctuations affects the geometric phase in
a different way than the dynamical phase. We have experimentally tested the robustness of Berrys geometric phase for spin-1/2 particles in a cyclically varying magnetic field. Using trapped polarized ultra-cold neutrons it is demonstrated that the geometric phase contributions to dephasing due to adiabatic field fluctuations vanish for long evolution times.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
