Numerical studies of superfluids and superconductors
Numerical studies of superfluids and superconductors
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超流体和超导体的数值研究
DOI：
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发表时间：
2001
期刊：
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通讯作者：
T. Winiecki
中科院分区：
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作者：
T. Winiecki
在本论文中，我们通过数值求解与超流性和超导性相关的各种基本问题，展示了 Gross-Pitaevskii 和瞬态 Ginzburg-Landau 方程的强大功能。我们首先研究大质量物体通过格罗斯-皮塔耶夫斯基方程建模的量子流体的运动。低于临界速度，物体不会与流体交换动量或能量。这是其超流性质的体现。我们讨论了向物体施加恒定力的效果，并表明，对于较小的力，会产生一个涡环，物体会附着在涡环上。对于较大的力，物体与涡环分离，我们观察到环的周期性脱落。传递到系统的所有能量都包含在涡流环内，物体上的阻力是由于涡流发射的反冲力造成的。如果我们超过声速，声音发射产生的阻力就会产生额外的影响。为了与超导性联系起来，我们讨论旋转系统中的涡旋态。在基态下，可以观察到规则的涡旋阵列，对于包含许多涡旋的系统，模拟固体旋转。在论文的第二部分，我们首先回顾了外加磁场中金兹堡-朗道方程的解。对于超导盘，我们观察到类似于旋转超流体中的涡旋阵列。最后，我们研究在外部磁场作用下沿着超导线流动的电流。我们观察洛伦兹力引起的磁通线的运动，以及由此产生的耗散。我们测量 V – I 曲线，类似于超流体中的阻力。随着杂质的引入，磁通线被钉扎，从而导致临界电流增加。
In this thesis we demonstrate the power of the Gross-Pitaevskii and the time-dependent Ginzburg-Landau equations by numerically solving them for various fundamental problems related to superfluidity and superconductivity. We start by studying the motion of a massive object through a quantum fluid modelled by the Gross-Pitaevskii equation. Below a critical velocity, the object does not exchange momentum or energy with the fluid. This is a manifestation of its superfluid nature. We discuss the effect of applying a constant force to the object and show that for small forces a vortex ring is created to which the object becomes attached. For a larger force the object detaches from the vortex ring and we observe periodic shedding of rings. All energy transfered to the system is contained within the vortex rings and the drag force on the object is due to the recoil of the vortex emission. If we exceed the speed of sound, there is an additional contribution to the drag from sound emission. To make a link to superconductivity, we then discuss vortex states in a rotating system. In the ground state, regular arrays of vortices are observed which, for systems containing many vortices, mimic solid-body rotation. In the second part of the thesis, we initially review solutions to the Ginzburg-Landau equations in an applied magnetic field. For superconducting disks we observe vortex arrays similar to those in rotating superfluids. Finally, we study an electrical current flow along a superconducting wire subject to an external magnetic field. We observe the motion of flux lines, and hence dissipation, due to the Lorentz force. We measure the V – I curve which is analogous to the drag force in a superfluid. With the introduction of impurities, flux lines become pinned which gives rise to an increased critical current.