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Author |
Magnus, W.; Brosens, F. |
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Title |
Occupation numbers in a quantum canonical ensemble : a projection operator approach |
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A1 Journal article |
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Year  |
2019 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
518 |
Issue |
518 |
Pages |
253-264 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is (1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and (2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons. (C) 2018 Elsevier B.V. All rights reserved. |
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Wos |
000456359200021 |
Publication Date |
2018-11-28 |
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Series Issue |
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Edition |
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ISSN |
0378-4371 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
1 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243 |
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Call Number |
UA @ admin @ c:irua:157468 |
Serial |
5223 |
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Author |
Pereira, J.R.V.; Tunes, T.M.; De Arruda, A.S.; Godoy, M. |
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Title |
Thermal properties of the mixed spin-1 and spin-3/2 Ising ferrimagnetic system with two different random single-ion anisotropies |
Type |
A1 Journal article |
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Year |
2018 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
500 |
Issue |
500 |
Pages |
265-272 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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Abstract |
In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins S-A = 1 in the sublattice A and S-B = 3/2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J < 0). We used two random single-ion anisotropies, D-i(A) and D-j(B), on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature T-c versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution. (C) 2018 Elsevier B.V. All rights reserved. |
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Place of Publication |
Amsterdam |
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Wos |
000430027400025 |
Publication Date |
2018-02-21 |
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ISSN |
0378-4371 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
3 |
Open Access |
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Notes |
; The authors acknowledge financial support by the Brazilian agencies CNPq, Brazil, CAPES, Brazil (Grant No. 88881.120851/2016-01) and FAPEMAT, Brazil. ; |
Approved |
Most recent IF: 2.243 |
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Call Number |
UA @ lucian @ c:irua:150706UA @ admin @ c:irua:150706 |
Serial |
4985 |
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Author |
Magnus, W.; Lemmens, L.; Brosens, F. |
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Title |
Quantum canonical ensemble : a projection operator approach |
Type |
A1 Journal article |
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Year |
2017 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
482 |
Issue |
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Pages |
1-13 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function Z(N) and the Helmholtz free energy F-N as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 – F-N, as illustrated for a two-dimensional fermion gas. (C) 2017 Elsevier B.V. All rights reserved. |
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Place of Publication |
Amsterdam |
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Wos |
000405885500001 |
Publication Date |
2017-04-20 |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0378-4371 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
1 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243 |
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Call Number |
UA @ lucian @ c:irua:145145 |
Serial |
4722 |
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Author |
Magnus, W.; Nelissen, K. |
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Title |
Quantum diffusion: A simple, exactly solvable model |
Type |
A1 Journal article |
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Year |
2015 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
417 |
Issue |
417 |
Pages |
96-101 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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Abstract |
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact, analytical solution of the model yields the transient behavior of the coupled fermion systems evolving to a final steady state, whereas the long-time behavior is determined by a power law rather than by exponential decay. Similar results are obtained for the entropy production which is proportional to the diffusion current. (C) 2014 Elsevier B.V. All rights reserved. |
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Place of Publication |
Amsterdam |
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Language |
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Wos |
000345721800011 |
Publication Date |
2014-09-28 |
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Edition |
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ISSN |
0378-4371; |
ISBN |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
2.243 |
Times cited |
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Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243; 2015 IF: 1.732 |
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Call Number |
c:irua:122170 |
Serial |
2777 |
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Author |
Sels, D.; Brosens, F.; Magnus, W. |
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Title |
Wigner distribution functions for complex dynamical systems : a path integral approach |
Type |
A1 Journal article |
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Year |
2013 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
392 |
Issue |
2 |
Pages |
326-335 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
Starting from Feynmans Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynmans and Vernons influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators. As an example we calculate the propagator for the reduced Wigner function associated with the CaldeiraLegett model. |
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Place of Publication |
Amsterdam |
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Wos |
000311135200004 |
Publication Date |
2012-09-14 |
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Edition |
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ISSN |
0378-4371; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
9 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243; 2013 IF: 1.722 |
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Call Number |
UA @ lucian @ c:irua:101414 |
Serial |
3921 |
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Author |
Sels, D.; Brosens, F.; Magnus, W. |
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Title |
Classical trajectories : a powerful tool for solving tunneling problems |
Type |
A1 Journal article |
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Year |
2012 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
391 |
Issue |
1/2 |
Pages |
78-81 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
In the realm of Ehrenfests theorem, classical trajectories obeying Newtons laws have been proven useful to construct explicit solutions to the time-dependent WignerLiouville equation. Whereas previous works have particularly focused on the initial distribution function as a vehicle found to carry the signatures of quantum statistics into the time-dependent solution, the present paper shows that the LagrangeCharpit method based on classical trajectories can be successfully invoked as well to tackle quantum mechanical features with no classical counterpart, such as tunneling. |
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Place of Publication |
Amsterdam |
Editor |
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Wos |
000297230700010 |
Publication Date |
2011-08-25 |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0378-4371; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
7 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243; 2012 IF: 1.676 |
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Call Number |
UA @ lucian @ c:irua:92359 |
Serial |
370 |
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