理想忆阻器的简单测试
A simple test for ideal memristors
摘要：
理想的忆阻器被定义为具有记忆的电阻器，当经受时间相关电流$I(t)$时，其电阻$R_M(q)$仅取决于流过其的电荷\it，使得其电压响应为$V(t)=R_M(q)I(t)$。有人认为，这些理想忆阻器的清晰指纹是它们的I-V曲线中的收缩磁滞回线。然而，箍缩的I-V磁滞回线不是具有记忆的电阻器是否真正是理想忆阻器的决定性测试，因为这样的性质也被其他电阻器共享，其记忆取决于除电荷之外的附加内部状态变量。在这里，我们介绍了一个非常简单和{ \it明确}的测试，可以用来检查实验，如果一个电阻器的记忆确实是一个理想的忆阻器。我们的测试是基于电容器-忆阻器电路的对偶性质，由此，对于忆阻器的任何初始电阻状态和任何形式的施加电压，理想忆阻器的最终状态必须与其初始状态相同，如果电容器电荷最终返回到其初始值。在实际实验中，足够宽的电压幅值和初始状态范围足以进行测试。提出的测试可以帮助解决文献中仍然存在的一些长期存在的争议，即理想的忆阻器是否确实存在，或者它是一个纯粹的数学概念。
英文摘要：
An ideal memristor is defined as a resistor with memory that, when subject to a time-dependent current, $I(t)$, its resistance $R_M(q)$ depends {\it only} on the charge $q$ that has flowed through it, so that its voltage response is $V(t)=R_M(q)I(t)$. It has been argued that a clear fingerprint of these ideal memristors is a pinched hysteresis loop in their I-V curves. However, a pinched I-V hysteresis loop is not a definitive test of whether a resistor with memory is truly an ideal memristor because such a property is shared also by other resistors whose memory depends on additional internal state variables, other than the charge. Here, we introduce a very simple and {\it unambiguous} test that can be utilized to check experimentally if a resistor with memory is indeed an ideal memristor. Our test is based on the duality property of a capacitor-memristor circuit whereby, for any initial resistance states of the memristor and any form of the applied voltage, the final state of an ideal memristor must be identical to its initial state, if the capacitor charge finally returns to its initial value. In actual experiments, a sufficiently wide range of voltage amplitudes and initial states are enough to perform the test. The proposed test can help resolve some long-standing controversies still existing in the literature about whether an ideal memristor does actually exist or it is a purely mathematical concept.
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